key: cord-0974467-xib7tz1m authors: Musa, Salihu S.; Qureshi, Sania; Zhao, Shi; Yusuf, Abdullahi; Mustapha, Umar Tasiu; He, Daihai title: Mathematical modeling of COVID-19 epidemic with effect of awareness programs date: 2021-02-18 journal: Infect Dis Model DOI: 10.1016/j.idm.2021.01.012 sha: 8d7c88a5186c4f539bca4be1b3d6b2880953335c doc_id: 974467 cord_uid: xib7tz1m Severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) is a novel virus that emerged in China in late 2019 and caused a pandemic of coronavirus disease 2019 (COVID-19). The epidemic has largely been controlled in China since March 2020, but continues to inflict severe public health and socioeconomic burden in other parts of the world. One of the major reasons for China's success for the fight against the epidemic is the effectiveness of its health care system and enlightenment (awareness) programs which play a vital role in the control of the COVID-19 pandemic. Nigeria is currently witnessing a rapid increase of the epidemic likely due to its unsatisfactory health care system and inadequate awareness programs. In this paper, we propose a mathematical model to study the transmission dynamics of COVID-19 in Nigeria. Our model incorporates awareness programs and different hospitalization strategies for mild and severe cases, to assess the effect of public awareness on the dynamics of COVID-19 infection. We fit the model to the cumulative number of confirmed COVID-19 cases in Nigeria from 29 March to 12 June 2020. We find that the epidemic could increase if awareness programs are not properly adopted. We presumed that the effect of awareness programs could be estimated. Further, our results suggest that the awareness programs and timely hospitalization of active cases are essential tools for effective control and mitigation of COVID-19 pandemic in Nigeria and beyond. Finally, we perform sensitive analysis to point out the key parameters that should be considered to effectively control the epidemic. In Nigeria, the most populous country in sub-Saharan Africa, whose health care system does not provide basic and regular health services adequately for its citizens even in normal situations; hit by the double burden from COVID-19 and other infectious and non-infectious diseases (NCDC, 2020) . Notwithstanding, in its trying to tackle the pandemic situation in the country, the Nigeria government considered some basic measures prior to the first case detection in 27 February 2020 and still modifying them according to WHO recommendations (WHO, 2020a; Gilbert et al., 2020; NCDC, 2020) . These measures include improving health institutions, creation of isolation and quarantine centers to treat/isolate COVID-19 patients, borders and schools closures, creation of awareness and enlightenment programs at different levels and in different methods, and resource support mobilization from different groups to assist the J o u r n a l P r e -p r o o f community, especially the most vulnerable individuals, in order to facilitate the control and prevention of the disease at different levels. The total number of active cases and deaths of COVID-19 in Nigeria recorded by the Nigeria Centre for Disease Control (NCDC) as of January 25, 2021 were 122,996 and 1,507, respectively (NCDC, 2020). Currently, there is no safe and effective vaccine or antiviral treatment for use against the COVID-19 infection. Therefore, the control of COVID-19 are currently directed primarily on applying set of non-pharmaceutical interventions (NPIs) measures, as well as use of treatments to improve the immune systems of infected individuals (WHO, 2020a; CDC, 2020). The fact that the management and mitigation efforts to halt or reduce the spread of the COVID-19 pandemic are largely focused on implementing non-pharmaceutical interventions (NPI), such as social or physical distancing, community-wide lock-down, contact tracing, dissemination of health education knowledge on COVID-19 (awareness programs), quarantine of suspected cases, isolation of confirmed cases and use of face-masks (18, 19) . presented. Sensitivity analysis is presented in section 5. Section 6 present detailed discussion of the research study conducted in the present work. The time series case data of the COVID-19 are extracted from the Nigeria Center for Disease Control (NCDC) (NCDC, 2020) from March 29 to June 12, 2020. All cases are laboratory confirmed following the case definition by the NCDC situation report. Clinical diagnosis of suspected individuals was used as the criterion for confirmed cases since February 2020 (NCDC, 2020). The confirmed case is defined as the individual whose real-time reverse transcription polymerase chain reaction (rRT-PCR) result turned out to be positive. A new deterministic epidemic model is developed based on the standard SEIR model to study the transmission dynamics of COVID-19 outbreak. We split the total human population at time , It is worth knowing that our model did not capture birth and death rates due to the relative short period of the epidemic, which started in early 2020 in Wuhan, China. Our model considers person-to-person mode of transmission as the potential transmission route and ignored other routes due to their less impact in community transmission. The model flow diagram is shown in Figure 1 , and the state variables and the model parameters (all positive) are summarized in Table 1 . Our model equations are given by following nonlinear system of ordinary differential (1) In particular, the term J o u r n a l P r e -p r o o f where H G = + , + -+ . + / , , H I = + 1 2 + 3, H J = + 1 4 + 0 + / 1 4 , = (i.e., at DFE = since we considered closed population) and . * (spectral radius) is defined as the maximum of the absolute values of the eigenvalues of the matrix DE FG . Hence, the result given below follows Theorem 2 of (van den Driessche & Watmough, 2002). Thus, the epidemiological implication of the above theorem is that a small influx of COVID-19 cases will not generate a large COVID-19 outbreaks if the is below unity. J o u r n a l P r e -p r o o f Validation of a newly proposed epidemiological model is one of the crucial process to examine a disease's transmission dynamics. Availability of real data for the underlying disease greatly helps to complete this task of validation, these data also assist to get best values of some unknown biological parameters involved in the model. Therefore, we have carried out this approach via attains a minimum. There are 17 biological parameters associated with the proposed model. Some of them have been obtained from available literature whereas the, rest have been best fitted. As can be seen in the Table 2, the (3). Whenever the reported data come under the fitted curve then residues will be shown below that horizontal line (blue color line in (b) part of the Figure 2) and similarly when the reported data lie above the fitted curve then residues will be shown above that horizontal line (blue color line in (b) part of the Figure 2) . The numbers for residues show the vertical distance between reported data and fitted curve. Moreover, when such residues are observed to be scattered then the fitting is justified. In other words, if the residuals appear to behave randomly, it suggests that the model fits the data well. This is what happens in the Figure 2 . The detailed explanation on fitting models on data with residual analysis can be found in (11) . Finally, the basic reproductive number ( ) is estimated as = 9.1235\ − 01 (95% : 5.8725\ − 02 − 2.8728) using the parameters presented in the Table 2 . This result is largely consistent with previous estimate on the basic reproduction number ( ) in Africa (8) In the Figure 3 Table 2 . Here, we consider the hypothetical scenario where COVID-19 begins to spread more rapidly in unaware susceptible area (unaware susceptible region) than in low prevalence area (aware susceptible region) where the outbreak could be eradicated faster likely due to following of common non-pharmaceutical control health measures recommended by the WHO, see Figure 4 and 5 (a-d). The results indicate that lack of proper and constant awareness program of susceptible and exposed individuals could lead to a larger prevalence of COVID-19 especially in a country with already overwhelmed health care system such as Nigeria. This further illustrates that adequate awareness and enlightenment programs in a most vulnerable communities is a good way to fight against the disease especially in countries with poor health care systems. Table 2 . Table 2 . In this scenario (Figure 6 ), we obtained some contour plots for the basic reproductive number, , as a function of two different epidemiological parameters chosen from the Table 1 . Figure 6 (a)-(f) indicates that the parameters %, ), 3, a and 0 seems very significant (vital) and should be J o u r n a l P r e -p r o o f considered in mitigating the COVID-19 pandemic in Nigeria. In Figure 6 (a), we showed that the basic reproduction number, , increases with respect to the increase in $, and the % as expected. In Figure 6 In this section, sensitivity analysis is carried out using the partial rank correlation coefficients (PRCCs) for ranking the significance of each parameter output through determining the target biological quantities/parameters, i.e., the basic reproduction number and the infection attack rate as response functions (see, Figure 7 ) (Gao et al., 2016) , to get insight into designing effective control measures or strategies to combat the epidemic. Using the parameters' values given in Table 2 Table 2 . The circle dots (in purple) are the estimated correlations and the bars are the 95% CIs. Since early 2020, the world has been facing a devastating COVID- 19 J o u r n a l P r e -p r o o f None. 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Ltd. CollaborativeResearch project. The second author (SQ) is thankful to Mehran University of Engineering and Technology for providing necessary sources required to carry out this research work. The authors are grateful to the handling editor and anonymous reviewers for their helpful comments which were used to improve and straighten initial draft of the article. J o u r n a l P r e -p r o o f Highlights • We proposed a mathematical model with effect of awareness programs and different hospitalization schemes to study the transmission dynamics of COVID-19 epidemic.• We analyzed the model and estimate key epidemiological parameters that are useful in controlling the epidemic in Nigeria.• We assess the effect of awareness programs by simulating the model and varying awareness programs related parameters to explore its impact with respect to the basic reproduction number.• We fit the model to the cumulative number of laboratory confirmed cases in Nigeria from March 29 to June 12, 2020, for COVID-19 epidemic to show the trends of the epidemic.