key: cord-1019207-nmo1x4p8 authors: Senapati, Abhishek; Rana, Sourav; Das, Tamalendu; Chattopadhyay, Joydev title: Impact of intervention on the spread of COVID-19 in India: A model based study date: 2021-04-20 journal: J Theor Biol DOI: 10.1016/j.jtbi.2021.110711 sha: 68a39e918bc0ff4dfc85a12e1ccb71bf8c986f32 doc_id: 1019207 cord_uid: nmo1x4p8 The outbreak of coronavirus disease 2019 (COVID-19), caused by the virus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has already created emergency situations in almost every country of the world. The disease spreads all over the world within a very short period of time after its first identification in Wuhan, China in December, 2019. In India, the outbreak, starts on 2 nd March, 2020 and after that the cases are increasing exponentially. Very high population density, the unavailability of specific medicines or vaccines, insufficient evidences regarding the transmission mechanism of the disease also make it more difficult to fight against the disease properly in India. Mathematical models have been used to predict the disease dynamics and also to assess the efficiency of the intervention strategies in reducing the disease burden. In this work, we propose a mathematical model to describe the disease transmission mechanism between the individuals. Our proposed model is fitted to the daily new reported cases in India during the period 2 nd March, 2020 to 12 th November, 2020. We estimate the basic reproduction number, effective reproduction number and epidemic doubling time from the incidence data for the above-mentioned period. We further assess the effect of implementing preventive measures in reducing the new cases. Our model projects the daily new COVID-19 cases in India during 13 th November, 2020 to 25 th February, 2021 for a range of intervention strength. We also investigate that higher intervention effort is required to control the disease outbreak within a shorter period of time in India. Moreover, our analysis reveals that the strength of the intervention should be increased over the time to eradicate the disease effectively. counts in various states of India has also been studied [35, 36] . 75 In this work, we propose a deterministic compartmental model to de-76 scribe the disease transmission mechanism between the individuals. We con-77 sider the outbreak situation of India during the period from 2 nd March, 2020 78 to 12 th November, 2020 and our model is fitted to the daily new reported 79 cases. In this study, we explore several important aspects of the disease dy- The rest of the paper is organized as follows. In section 2, we briefly 93 describe our proposed model. Section 3 is devoted in describing the procedure 94 of model fitting. The estimation of basic reproduction number, effective 95 reproduction number and epidemic doubling time from actual incidence data 96 is described in section 4. In section 5, the efficiency of the intervention is 97 studied. Finally we discuss the findings obtained from our study in section 6. 98 2. Description of the model 99 We adopt deterministic compartmental modelling approach to describe 100 the disease transmission mechanism. Depending on the health status, the 101 total human population is categorized into seven compartments: susceptible 102 (S), exposed (E), symptomatic (I), asymptomatic (I a ), quarantined (I q ), 103 hospitalized (H) and recovered (R). Susceptible population becomes exposed 104 with the disease after experiencing close contacts with the symptomatic as well as asymptomatic individuals. We assume that the rate of disease transmission from asymptomatic individuals to susceptible individuals is less than represents the transmission dynamics of the disease: (2.1) The schematic diagram and the description of the parameters used in the 150 model (2.1) is presented in Fig. 1 March, 2020 to 12 th November, 2020 and our model is fitted to the daily re- March, 2020 to 24 th July, 2020,(ii.) 25 th July, 2020 to 12 th September, 2020, 182 (iii.) 13 th September, 2020 to 12 th November, 2020 and estimate the value 183 of intervention strength k separately for each phase. The daily new reported cases from the model is given by where Θ = {β, η, ρ 1 , ρ 2 , k}. 186 We perform our model fitting by using in-built function lsqnonlin in MAT-187 LAB (Mathworks, R2014a) to minimize the sum of square function. In our 188 case, the sum of square function SS(Θ) is given by, where, N d (t i ) is the actual data at t th i day and n is the number of data points. The model fitting to the daily new reported cases is displayed in Fig. 2 . The 191 values of the estimated parameters are given in Table 1 . The control reproduction number, R c is defined as the spectral radius of It is to be noted that, the first term is the number of new infection caused (4.4) Here we first estimate the force of infection Λ and then estimate R 0 by Step 1. We plot the number of new COVID-19 cases (per day) in x−axis versus 238 the cumulative number of COVID-19 cases (per day) in y − axis. Step 2. In the scatter plot, we point out the threshold of cumulative cases up 240 to which new cases show the exponential growth. Step 3. Then we fit a linear regression model using the least square technique 242 to this exponential growth data. Step 4. The slope of the fitted line is considered as the force of infection (Λ). 244 We obtain Λ = 0.0324±0.00028 day −1 based on the slope of the estimated 245 line shown in Fig. 3 the initial transmissibility of COVID-19 is pretty much higher than 1, which 249 in turns implies that it is essential to control the disease at the initial phase. there is a risk of huge number people becoming infected within that time. Therefore, it is necessary to apply some preventive measures, else there will 259 be a large outbreak in the above mentioned period. The parameter values are taken from Table 1 . In this section, we study the effect of intervention strategies (e.g. lock- November, 2020 and estimated the strength of intervention k (see Table 1 ) Table 2 ). Now, if the strength of interven-317 tion is slightly increased (i.e for k = 0.8), then significant reduction in the 318 cases is observed (see Fig. 5 ). It is also to be noted from Table 2 ). 323 We also observe that if the intervention strength is reduced from its baseline 324 value, say for k = 0.7, the total number of new cases during the projec- the number of new cases starts to grow exponentially (see Fig. 5 ). In such a 328 scenario, the total new cases at the end of 25 th February, 2021 is projected 329 to be 8.0140 million (see Table 2 ). The final cumulative new cases with respect to intervention strength (k) 331 is shown in Fig. 6 . We observe that a rapid change occurred for k ∈ [0.6, 0.7]. Table 2 ). Also if we reduce the intervention strength by 10.73% (i.e for 345 k = 0.65) from its baseline value, the final cumulative new cases is increased 346 by 65% (see Table 2 ). For k ∈ (0.7282, 0.95], we see that up to 60% reduction 347 in the final cumulative cases can be achieved. More specifically, 9.86% (i.e 348 for k = 0.80) and 23.59% (i.e for k = 0.90) increment in k, leads to 43% 349 and 60% reduction in the cumulative cases respectively (see Table 2 ). 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