key: cord-0963470-my95tdu9
authors: Singh, A.; Bajpai, M. K.
title: SEIHCRD Model for COVID-19 spread scenarios, disease predictions and estimates the basic reproduction number, case fatality rate, hospital, and ICU beds requirement
date: 2020-07-27
journal: nan
DOI: 10.1101/2020.07.24.20161752
sha: 5b43b5fc42f88c116f993b26b075792e7a1c66d2
doc_id: 963470
cord_uid: my95tdu9

We have proposed a new mathematical method, SEIHCRD-Model that is an extension of the SEIR-Model adding hospitalized and critical twocompartments. SEIHCRD model has seven compartments: susceptible (S), exposed (E), infected (I), hospitalized (H), critical (C), recovered (R), and deceased or death (D), collectively termed SEIHCRD. We have studied COVID- 19 cases of six countries, where the impact of this disease in the highest are Brazil, India, Italy, Spain, the United Kingdom, and the United States. SEIHCRD model is estimating COVID-19 spread and forecasting under uncertainties, constrained by various observed data in the present manuscript. We have first collected the data for a specific period, then fit the model for death cases, got the values of some parameters from it, and then estimate the basic reproduction number over time, which is nearly equal to real data, infection rate, and recovery rate of COVID-19. We also compute the case fatality rate over time of COVID-19 most affected countries. SEIHCRD model computes two types of Case fatality rate one is CFR daily and the second one is total CFR. We analyze the spread and endpoint of COVID-19 based on these estimates. SEIHCRD model is time-dependent hence we estimate the date and magnitude of peaks of corresponding to the number of exposed cases, infected cases, hospitalized cases, critical cases, and the number of deceased cases of COVID-19 over time. SEIHCRD model has incorporated the social distancing parameter, different age groups analysis, number of ICU beds, number of hospital beds, and estimation of how much hospital beds and ICU beds are required in near future.

The world is fighting against a new enemy in these days, which is the COVID-19 virus. The COVID-19 disease, known as coronavirus disease in 2019. The virus has spread quickly in the world since its first appearance in China. We all are fighting every day against all the economical and social implications because of this virus and most of the countries are facing this new enemy in the Western countries.

COVID-19 has a profound impact on the economy of all countries. Global stock markets fell on 24 February 2020 because of the rapid increase in the number of cases of COVID-19 across mainland China [41, 42] . The world has seen the financial crisis first-time a huge decline in stock markets after 2008 and it crashed in March 2020 [43] [44] [45] and because of this pandemic, many financial deals are being canceled or postponed [46] . This paper proposed a new mathematical model to study the dynamics of transmission and control of the COVID-19 pandemic in most affected countries. The SEIR model is a widely used epidemiological model based on the SIR model, which was given, by Kermack and Mckendrick [47] . Kermack and Mckendrick's epidemic model has been very effective in forecasting outbreak behavior quite close to that seen in several reported epidemics [48] . After Kermack and Mckendrick's manuscript, many epidemic mathematical models have been developed stochastic models, discrete-time models, continuous-time models, and diffusion models. Compartmental models primarily depend on differential equations. These models are normally subdivided into many compartments (i.e., Susceptible, Infected, Recovered, Critical, Death, etc.). Compartmental models focused on basic law defining the transition of people from one compartment to another. These Models use mathematics to find the different parameters to estimate the effect of different interventions. Modeling can help determine which intervention to stop and which to continue and can predict the future [49] . The model can predict how disease spreads, what will be the lifetime of any epidemic, how much people infected, recovered, and deceased. It can also estimate many parameters like reproduction numbers etc. These models are used in many applications nowadays mostly in epidemiology, and many other fields like economics, politics, social science, and in the medical field. Epidemiological models such as SEIR provide a valuable computational approach to understanding the microscopic view of the spread of disease. These models play an important role to measure possible strategies for the control and mitigation of infectious diseases [49] [50] [51] . These models are useful in cases where disease dynamics are not unclear. It estimates the number of cases in worst and best-case scenarios. Mathematical models are also helpful in understanding the scenario for spreading the disease [52] [53] [54] .

The SEIR model failed to estimate the spread where preventive measures are adopted such as social distancing, different age groups, number of ICU beds, number of hospital beds, and mortality rate. The mathematical model is very helpful to predict the disease outbreak of COVID-19 and the SIR model and SEIR model have been widely used for prediction. SEIHCRD model is the modification of the SEIR model. The present manuscript encompasses a new modified SEIR model which estimates the spread of COVID-19 spread, including all the parameters mentioned above.

We have proposed a model for forecasting under uncertainties, constrained by various observed data. The model allows studying scenarios for the progress of disease spreading. SEIHCRD model estimates the date and magnitude of peaks of corresponding to exposed people, the number of infected people, the number of people hospitalized, the number of people admitted in ICUs, and the number of death of COVID-19.

The proposed model has incorporated the social distancing parameter, different age groups analysis, number of ICU beds, number of hospital beds and lockdown effect gives a more accurate estimation of how much hospital beds and intensive care unit (ICU) beds are required in near future. Also, the proposed model analyzes the reproduction number of most affected countries and when the disease goes settle. The basic reproduction number for COVID-19 in January was between 1.4 and 2.5 [55] , but later analysis showed that this can vary from 3.8 to 8.9 [56] . As of last May 2020, the spread of disease in most of the countries is either stable or decreasing [57] .

The structure of this paper is as follows; Section 1 introduces COVID-19 and explains the significance of this research. The SEIHCRD model for COVID-19 spread estimation; predictive modeling has been presented in section 2. Section 3 has discussed the data analysis and parameter estimation used for validating proposed mathematical models. Results and discussions of the proposed model have been discussed in section 4. Finally, the conclusion and some future works have been discussed in Section 5.

The SIR and SEIR compartmental models are the most commonly used mathematical method for infectious disease. SEIHCRD-Model is a new mathematical method that is an extension of the SEIR-Model adding death, hospitalized, and critical compartments. The proposed method and some basic compartmental models have been described below.

Mathematical modeling of infectious disease specially Coronavirus disease (COVID-19) has been a trending topic for many epidemiologists and data scientists in the last some weeks. Coronavirus disease (COVID-19) is an infectious disease hence it can spread from one member of the population to another member of the population. Kermack-McKendrick [47] has proposed the SIR (susceptible, infected, recovered) model in 1927. SIR model is separated into three population-wise compartments of Susceptible (S), Infectious (I), and Recovered (R). SIR model describes the transition of people from Susceptible to Infected and then Infected to Recovered based on underlying parameters, which controls disease dynamics in the population. Deceased cases come under the Recovered compartment in the SIR model. The SIR model is shown in Fig. 1 .

We write the model equations that are independent of the population of the country by considering the fraction of the people in each category. The rates of transfer from one category to another are the model parameters and a set of differential equations are formed. The SIR model has been described below using the coupled ordinary differential equations:

= .

(3)

Where, N -Total population S -A proportion of the entire population that is healthy and have never been infected I -A proportion of the entire population that is infected by the virus R -A proportion of the entire population that has recovered from the infection . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint Where initial conditions (S (0), I (0), R (0)) are not exactly known, and these systems of ordinary differential equations are extremely sensitive to the initial parameters. Description of some parameters are given below: η -social distancing factor β -the rate of transmission of infection from susceptible to infected γ-the rate of recovery R 0 -basic reproduction number X -number of days an infected person has and can spread the diseases ( = ) Basic reproduction number = .

Therefore, from above we can write it as =

Kermack and McKendrick [47] , Beretta, and Takeuchi [58] have further developed their theories and proposed a time delay SIR model. Cooke and Driessche [59] investigated the incubation period in the spread of infectious diseases, introduced the "Exposed, E," compartment, and proposed a time delay model. SEIR model is separated into four population-wise compartments of Susceptible (S), Exposed (E), Infectious (I), and Recovered (R). SEIR model describes the transition of people from Susceptible to Exposed, then Exposed to Infected and then Infected to Recovered based on underlying parameters, which controls disease dynamics in the population. The SEIR model is shown in Fig. 2 .

Deceased cases come under the recovered compartment in the SEIR model. Deceased cases play an important role in infectious modeling hence; we have to make it a separate compartment. The extension of the SEIR model is the SEIRD model in which the Dead compartment is added. SEIR model is separated into four population-wise compartments of Susceptible (S), Exposed (E), Infectious (I), Recovered (R), and Dead (D). SEIRD model describes the transition of people from Susceptible to Exposed, then Exposed to Infected, then Infected to Recovered and Infected to Dead. The SEIRD model is shown in Fig. 3 .

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The SEIR model is described below using the coupled ordinary differential equations:

= . − .

= .

(3)

Where E -A proportion of the entire population that is exposed to infection, transmit the infection and turn into either Symptomatic or purely Asymptomatic, and not detected Description of some parameters used in the SEIR model is given below: β-the rate of transmission of infection from susceptible to exposed δ-the rate of transmission of infection from exposed to infectious and the rest of the parameters are the same as the SIR model.

And after adding dead compartment ordinary differential equations are change accordingly, hence coupled ordinary differential equations of SEIRD Model are given below: 

= + + + +

Here D -A proportion of the entire population that is dead because of the infection.

Description of some parameters used in the SEIRD model is given below: ρ -Median time from Infected to Death γ -recovery period and the rest of the parameters are the same as the SIR model.

The present manuscript encompasses two new compartments added for more accurate analysis is the Hospitalized compartment and the Critical compartment. This model allows overflowing hospitals. SEIHCRD model is separated into seven population-wise compartments of Susceptible (S), Exposed (E), Infectious (I), Hospitalized (H), Critical (C), Recovered (R), and Dead (D). SEIRD model describes the . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint transition of people from Susceptible to Exposed, then Exposed to Infected, and then from Infected they can either Hospitalized or Recovered compartment. Of course, only infected individuals can enter the hospitalized compartment and critical compartment. From hospitalized, they can either Critical or Recover and from the Critical compartment, they can either die or recover. The SEIHCRD model is shown in Fig. 4 .

Some infections are mild like fever, cough, and may even have mild pneumonia but do not require hospitalization. These individuals may recover or in the future, they go to the hospitalized compartment.

People with a serious infection, suffer from severe pneumonia, and need hospitalization. These individuals may either recover or progress to the critical compartment. People with critical infection experience multi-organ failure and multiple disorders require treatment in an ICU. These people either recover from the disease or die from it.

The SEIHCRD model is described below using the coupled ordinary differential equations: 

= .

(1 − ( → )). + . (1 − ( → )). + (1 − ( → )).

= .

( → ).

= + + + + + +

Here H -A proportion of the entire population that is found positive in the test and hospitalized C -A proportion of the entire population those are seriously ill and who need ICU . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 27, 2020. We know that every country has limited resourced of hospital beds and ICUs. Sometimes the number of critical cases is more than the number of ICUs in this condition doctors have to choose who gets treated with the limited number of resources. This manuscript accepts all these conditions as follows.

If there is a B number of ICUs and C number of critical cases then following condition occurs:

1. If the number of ICUs is more than critical cases then all patients get treated. The SEIHCRD with critical case ordinary differential equations are:

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The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint = .

( → ). − .

Compartmental models are ordinary differential equations. These ordinary differential equations have required some initial conditions and parameters to solve and characterize ODE. The prevalence of COVID-19 in the compartment, the population has influenced by the complexities of many factors. Preliminary estimation of parameters helps solve important parameters such as fatality rate and basic reproduction rate, which will help us to have a more accurate understanding of the transmission trend of COVID-19. In the present manuscript, we first collect data for a specific period, then estimate the basic reproduction number, infection rate, and recovery rate of COVID-19, and based on these estimates, we analyze the spread and endpoint of COVID-19. η is the social distancing parameter. The social distancing parameter includes avoiding social gatherings and physical contact to avoid the spread of infectious disease. Its value lies in between zero to one. Everyone is quarantined if a lockdown is implemented and then its value is zero and they follow the normal routine without restriction then its value is one. R (0) and R0 are different quantities, R (0) describes the number of recovered at t = 0 whereas R0 is the basic reproduction number that is the ratio between the rate of contacts to the rate of recovery. The basic reproduction number is the expected number, which is spread by infected people in a population where all peoples are susceptible to infected.

R0 value is change with time, whenever any country implements lockdown the value of R0 decreases, and when that country removes lockdown its value starts increasing again. R0 value has decreased when any country puts strict lockdown and after some time it goes below one. R0 is the ratio of β and γ in the compartmental models, hence we can say that = .

. The value of R0 is R0_start before the lockdown and if the lockdown is imposed on day L then the value of R0 is decreased up to R0_end and the value of β is change accordingly.

Basic reproduction number R0 is not constant in real life it changes with time. The basic reproduction number value has changed accordingly if social distancing imposed. The model shows the initial impact of social distancing on the reproduction number. This model use, the logistic function on it because it changes very slowly initially, its speed increase when lockdown imposed, and then it slows down in the end. The reproduction number is

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The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint Description of parameters are given below:

-Value of R 0 on the first day -Value of R 0 on last day x 0 is the value of inflection point (i.e. the day when the value of R 0 decline drastically) η is the social distancing parameter.

According to the value of the social distancing parameter, it changes drastically.

The fatality rate is not stable it depends on many things. The fatality rate affects most by one of the common reasons is the Age factor, some fatal disease, and the number of ICU beds available, etc. The fatality rate is more when the most number of people are infected, and the fatality rate and is less when infected people are less. The base fatality rate is there when fewer people are infected.

Infected people become very much sometimes, at that time we need more medical equipment for treatment, sometimes everyone is not treated due to lack of medical facility. We should know what proportion of people are currently infected, hence we describe fatality rate φ as

Description of parameters are given below: s -It is arbitrary but the fixed value that controls the influence of infection (it chooses freely once and then stay constant over time)

φ opt -it is the optimal fatality rate I (t) is infected people at time t and N is the total population. The value of s controls the above equation. Therefore, carefully give the value of s.

Analysis of case fatality depends on Age group is complex. For this we separate different age groups (e.g. people aged 0 to 9, aged 10-19,…..aged 90-100) . for age group analysis we need two things. 1. Fatality rates by age group, 2. The proportion of the total population is in that age group.

The fatality rate is high if the population of old people is more, and if the proportion of young people is more, then the fatality rate is low. The fatality rate has calculated by:

So the overall fatality rate is a combination of the above two cases then,

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The copyright holder for this preprint this version posted July 27, 2020. . In the present manuscript, all the comorbidity cases are considered as critical cases. The fatality rate for all cases is shown in Tab. 3, and the proportion of age groups is shown in Fig. 14.

Every country has limited resourced of hospital beds and ICUs. Sometimes the number of critical cases are more than the number of ICUs in this condition doctors have to choose who gets treated with a limited number of resources. This manuscript accepts all these conditions as follows.

If there is a B number of ICUs and C number of critical cases then following condition occurs:

1. People with a serious infection, suffer from severe pneumonia and need hospitalization and hospital bed are available then they treated in the hospital but sometimes beds are not available due to shortage then they have to wait till the hospital bed is empty or self-quarantine in their home. 2. If the number of ICUs is more than critical cases then all patients are treated. 3. But if the number of ICUs are less than the number of critical cases (C>B) then B number of patient treated and rest (C-B) die because of shortage

The premise for hospital beds and ICUs is that countries respond and start constructing clinics and opening the rooms, etc., while the virus spreads. Hence, over time, the number of hospital beds and ICUs is increasing. We can model the number of beds as:

Description of parameters are given below:

Bedshosp0 -the total amount of Hospital beds available s -some scaling factor, and for ICUs

Description of parameters are given below:

Beds0 -the total amount of ICU beds available s -some scaling factor

As shown in the formula number of beds increases s times per day hence the value of s, plays an important role to calculate how many numbers of beds increase daily according to this patient's serve in the hospitals.

In this manuscript, we are focus on fitting the SEIHCRD Model with time-dependent basic reproduction number and age group based fatality rate, Hospital beds and ICUs with real COVID-19 data, that come close to the real data to find the parameters for our model that produce the possible prediction which is helpful in the future development.

All the experimental studies have been performed on the PYTHON platform using some important libraries i.e. pandas, NumPy, lmfit, ode, etc. The machine used for performing simulation work has Processor Intel(R) Core(TM) i7-5500U CPU @ 2.40 GHz, 2401 MHz, 2 Core(s), and 4 Logical Processor(s), 12 GB RAM hardware configuration.

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The curve-fitting model required some value initially for parameters. Initial guesses for parameters are very crucial. We need to know what parameters have known and what we have to get out of it. The proposed model has been used in many parameters. We have computed some parameters and considered some according to the present study and data. We do not need to fit N, just put the population of the place we have to model and similarly no need to calculate Beds0, just put the number of ICUs of the place we have to model. We have to give value to some parameters based on real data and analysis, i.e., Social distancing parameter η lies in the range zero and one, where zero indicates everyone is locked down and quarantined while one is for a normal life.

A Chinese study has shown the incubation period to be 5.2 days on average but it varies among different peoples [65] . The Chinese team study found 14 days of medical observation is necessary for those people who are exposed to pathogens. Median Hospital stay (χ=1/10) and recovery period (γ=1/10)

The JANA study has found that the median hospital stay is 10 days, and all those who discharged alive, and research showed the basic recovery period of the patient is 10 days [66, 67] .

The median time to development of pneumonia and other symptoms for hospitalization (Ψ=1/5) and hospital to ICU admission (σ=1/ 7). The median time from symptom onset to the development of pneumonia is approximately 5 days, [68, 69] and the median time from symptom onset to severe hypoxemia and ICU admission is approximately 7-12 days [69] [70] [71] [72] [73] . Median intensive care units (ICUs) length of stay (φ =1/8).

The median intensive care units (ICUs) length of stay for COVID-19 patients was approximately 8 to 13 days of respiratory support in a Chinese report [73] [74] . Hence the recovery time from critical is the same as ICU's length of stay that is 8 days (μ=1/8).

The case fatality rate (CFR) represents the proportion of cases who eventually die from the disease [75] . The basic formula of case fatality rate is = and sometimes this formula is corrected then = ( ) , where T = average time from case confirmation to death.

We know that ( ) can be calculated by basic reproduction number ( ) and γ hence, no need to find any separate parameter for . The beds scaling factor s can be fitted, it not affect much in the result because the amount of people who are treated because of lack of facility is very less as compared to the number of death. The proposed model has three probability estimates ( → ), ( → ) and

( → ) split up by age groups and weighted by the proportion of per age group. We will try to fit all above probabilities, which extremely close to the prediction obtained of special risk group such as diabetics, high blood pressure, heart disease, etc. now we have to fit all the probabilities ( → ), ( → ) and ( → ) and , , and are the parameters of ( ).

Johns Hopkins University Center for Systems Science and Engineering is the main source of data [60]. We have collected and cleaned data for age groups, probabilities, and ICU beds from UN Data [61].

A total number of Hospital beds and ICUs as per one lack peoples for topmost affected countries. The number of people per age group for topmost affected countries. Probabilities for prob(I→H), prob(H→C), and prob(C→D) per age groups but we use fitted probabilities and collect the data of the number of fatalities day wise from 22 January 2020 onwards.

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We only use the data of the number of fatalities, not total cases or active cases because the number of reported cases is not much accurate it depends on many factors like the number of test cases, etc, but the number of fatalities reported is more accurate.

We have to collect all the data and parameters first of all that we already know, then define some initial guesses and set the upper and lower bounds for those we don't know. We can change the upper and lower bound and initial guess according to the situation. We set Levenberg-Marquardt as a fit model after defining all parameters. Levenberg-Marquardt algorithm is the most important algorithm in data fitting [62, 63] . Lmfit library provides a high-level interface to non-linear optimization and curve-fitting problems for Python [64] . R-squared value is a measure of how close the data are to the fitted line. R-squared value is always between zero and one. In general, the higher the R-squared value, the better the model fits your data. Curve fitting of death cases of India and Brazil is shown in Fig. 6 . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 27, 2020. 3. 4.7% as critical and can include respiratory failure, septic shock, and multi-organ failure. 4 . in about 2% of reported cases, the virus is fatal. 5 . The risk of death increases the older you are. 6 . Relatively few cases are seen among children.

Pre-existing illnesses that put patients at higher risk: . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The comorbidity fatality rate for all the cases has shown in Tab. 4 and the percentage showed that for a patient with a given pre-existing condition, the risk of dying if infected by COVID-19 [83] . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 27, 2020. . This dataset includes many countries' daily count of confirmed cases, recovered cases, and deaths. This time series dataset is available from 22 January 2020. We also gathered and crosschecked data in Worldometer, Coronavirus cases [81] , a website providing real-time data of COVID-19. These data are collected through public health authorities' announcements and are directly reported public and unidentified patient data, hence ethical approval is not required.

WHO has reported that 216 countries are affected by COVID-19. Fig. 7 shows that 35% of cases are from six countries only. The United States of America has the highest number of cases, which alone is 19% of the world. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Death cases are more accurate because rarely any case from COVID-19, which has not been registered. Fig. 8 shows that 39% of cases are from six countries only. The United States of America has the highest number of cases, which alone is 17% of the world. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint Case fatality rate: It is difficult to estimate the overall case fatality rate of an ongoing pandemic but we can calculate the daily fatality rate. Fig. 13 shows the Country wise daily case fatality rate from 01 March to 03 June 2020 of COVID-19. 

Italy and Spain in the 70 plus year-wise age category population is more percentage-wise, according to World Bank data. India and Brazil's population is higher in the age category of o to 20 years. Brazil, India, Italy, Spain, the United Kingdom, and the United States, the distribution of the population are almost equal between 20 and 70 age groups in all these countries. The population has distributed according to age category is shown in fig. 14 . is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Hospital beds or curative beds counting unit beds per 100,000 population or 100k population according to WHO and OECD. The basic measures focus on all the hospital beds, which are occupied or empty. The Country-wise number of hospital beds has shown in Fig. 15 . 

ICU beds counting unit is beds per 100,000 population or 100k population according to WHO and OECD. ICU beds have provided to all the cases with severe conditions. The Country-wise number of ICU beds is shown in Fig. 16 . is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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We have analyzed and predict the COVID-19 trend among the top affected countries of the world using our proposed SEIHCRD model in this section. Our proposed methods outcome shows Italy, Spain, the United Kingdom, the United stated of America have seen their worst time, now their conditions are improving. The peak of Brazil and India is yet to come in June and July month. Brazil will need hospital beds and ICU beds when the number of cases will become very high in the middle and last of June. Disease distribution in India is very random, e.g. Number of cases in Maharashtra and Delhi are very high in comparison to other states, some beds needed in June especially in Delhi state. Our method shows that Italy already suffers its peak now they shuttle down. The proposed model has shown that endpoint of USA cases in September, and UK cases will shuttle down in July. We have compared our proposed method results with real-world data, then it is largely the same.

Brazil has the second-highest in COVID-19 cases just behind the USA as of the starting of June 2020. COVID-19 cases will be at a peak in Brazil according to our proposed method in June and July. Basic reproduction number in nearly 4.5 in initial days, after some days it decreases, and after 220 days, it becomes one or even less. The case fatality rate has ups and down daily but it goes higher and higher up to 7.5 in our model and then slow down and total CFR is nearly 3.0 overall. The result of our proposed method shows that in Brazil, the number of cases will increase hence Brazil will need some Hospital beds and ICU beds in June, July, and August. A daily number of death cases on top of nearly 190 th day and goes up to 1800 people die per day, then slow down and shuttle down in October. The model has shown nearly 15 to 20 days, 700 hospital beds and 400 ICU beds required on-peak time. SEIHCRD Model results for Brazil has shown in Fig. 17 .

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The SEIHCRD model results show COVID-19 cases are on the peak in India around 200 th day (June last or July month) and there will no cases come at the end of September and October month. SEIHCRD-Model for India shows that the case fatality rate of COVID-19 in India is very low. Basic reproduction number R0 is nearly 2.0 in starting, it decreases after some time and falls slowly and after 170 days it is 1.3 that is nearly equal to the real scenario, and it goes down than one or even lower in the next 50 to 60 days. The daily Case fatality rate varies between 1.5, 3.0, and the overall case-fatality rate very steady after 200 days of nearly 2.0. India's geographical condition is completely different from the rest of the countries. The spread of COVID-19 disease is random in India. Maharashtra, Delhi Tamil Nadu, and . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Gujrat are most disease-affected states. According to the proposed model, June last and July starting the number of patients admitted to the hospital on the peak. Hospital beds and ICU beds have needed in June in India especially in Delhi states. Around the 200 th day when the cases are at peak then the number of death cases reaches 550 and the need of nearly 250 Hospital beds and ICU beds. SEIHCRD Model results for India are shown in Fig. 18 .

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SEIHCRD model result shows, Italy has seen its bad phase and now in a state of improvement and is trying to recover from that disastrous pandemic. Italy's healthcare system is the second-best in the world according to WHO. COVID-19 cases on a peak between 70 and 90 th days in Italy, and after 220 days its cases are very rare, and its cases almost stop coming in August. Basic reproduction number R0 starts from 5.0 and after about 100 days, the value of R0 starts decreasing visually. The number of death decrease drastically in the next few days after peak days. The proposed model for Italy showing that around 100 th day, the number of hospital beds and the number of ICU beds are required. That time the number of death cases is 800 per day and daily-hospitalized cases are nearly 2500. The Case fatality rate value reached 7.0, after that its value is reduced drastically in Italy. SEIHCRD Model results for Italy has shown in Fig. 19 .

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Spain has also gone through its worst phase. COVID-19 cases are on the peak in Spain around the 110 th day according to the SEIHCRD model, and after that, Spain recovered by this disaster rapidly in the next few days. The result shows that COVID-19 cases will not come in June last or July. The basic reproduction number is 7.0, after some time it reduces, and around 170 th day it goes to one and below. The Case fatality rate goes up to 7.0, after that its value reduced drastically and it gets one and below around 170 th day. In the proposed model for Spain showing that between 110 and 130 th days some hospital beds and ICU beds are required. At that, time the number of deaths is nearly 700 per day and daily-hospitalized cases are nearly 1250. SEIHCRD Model results for Spain has shown in Fig. 20 .

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SEIHCRD-Model for the United Kingdom shows that COVID-19 cases on peak around 140 th day and after that the United Kingdom has recovered by this disaster very fast in the next few days. After 240 days, its cases are very rare, and its cases almost stop in August. Basic reproduction number R0 starts from 4.5 and after about 120 th day, the value of R 0 starts decreasing visually. There are many ups and downs in the daily case fatality rate but it goes higher and higher up to 7.5 in our model and then slows down and total CFR is nearly 3.0 overall. SEIHCRD model has shown for the United Kingdom that some hospital beds and ICU beds have been required between the 100 th and 120 th days. That time the number of death is 1100 per day and daily-hospitalized cases are nearly 800. The population of old age people is more in the United Kingdom; it has been shown in the previous section. SEIHCRD Model results for the United Kingdom has shown in Fig. 22 .

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The WHO health has reported that the medical facility of the USA is good and they have more hospital beds and ICU beds for people in comparison to other countries by ratio. United States has the highest number of COVID-19 cases in the world. According to the SEIHCRD model for the United States of America COVID-19, cases are on a peak between 130 and 145 days after that it is improving, its speed is very slow but steady and cases stop in October. New York, California, Illinois, and New Jersey have the most affected states of the USA. The proposed model for the USA has shown that between 120 and 180 days, the number of hospital beds and the number of ICU beds required but its count is very low. That time the number of death has 1200 per day and daily-hospitalized cases have nearly 1400. The result shows the basic reproduction rate is 4.5 in starting after some time it decreases and goes up to one and even lower. The case fatality rate goes up to 8.0, after 200 days it drastically fell. Our proposed method shows that the . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint USA has the highest number of cases therefore, it takes more time in recovery. SEIHCRD Model results for the United States has shown in Fig. 23 .

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The copyright holder for this preprint this version posted July 27, 2020. 

Models are always simplifications of the real world. No models are perfect; there are some shortcomings in it. SEIHCRD Model also has some limitations, which are as follows:

Our system of differential equations is very sensitive to initial parameters. We have to very careful while given the initial parameters. Small changes in parameters can cause a huge difference in results. Our present manuscript has especially focused on serious cases and death cases. We have consented the serious cases that do not get treatment in the critical compartment. We have considered recovered cases not infected again in the future. R0 value cannot be increased; it either decreases or remain constant.

The mathematical model is very helpful to predict the disease outbreak of COVID-19 and the SIR model and SEIR model have been widely used for prediction. Our proposed SEIHCRD model is an extension of the SEIR model in which three-compartments has added that is death, hospitalized, and critical. People with a serious infection, suffer from severe pneumonia need hospitalization. These individuals may either recover or progress to the critical compartment. People with critical infection experience multi-organ failure and multiple disorders require treatment in an ICU. These people either recover from the disease or die from it.

The SEIHCRD model estimates the date and magnitude of peaks of corresponding to exposed people, the number of infected people, the number of people hospitalized, the number of people admitted in ICUs, and the number of death of COVID-19. The SEIHCRD model is time-dependent hence; we have calculated the number of cases infected cases, hospitalized cases, and critical cases with time. We have data of hospital beds and ICU beds of most infected countries by COVID-19 after that we have calculated the hospitalized cases and critical cases using the proposed model then after calculation we can say how much beds are . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 27, 2020. . https://doi.org/10.1101/2020.07.24.20161752 doi: medRxiv preprint required. SEIHCRD-Model also computes the basic reproduction number over time, which is nearly the same as real data, but sometimes it varies, we also compute the case fatality rate over time of COVID-19 most affected countries. The model computes two types of Case fatality rate one is CFR daily and the second one is total CFR. SEIHCRD model has shown, Spain and Italy have seen their worst times. The result shows that COVID-19 cases of Spain have ended completely in June last or July starting. Italy will be recovered completely by this disaster in August. India and Brazil have not yet seen the peak of the disaster. The result shows COVID-19 cases are at a peak in June in India and it is on a peak in June and July in Brazil. India needs some hospital beds in June. Brazil is going to have a shortage of hospital beds and ICU beds in June and July. The United State of America has suffered this tragedy the most. The USA has the highest number of total cases and deceased cases. The USA takes more days to recover and it will be recovered in October. The SEIHCRD model has shown the United Kingdom has also suffered this tragedy a lot, and it will be recovered in August.

The authors have no conflicts of interest to report regarding the present study."

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