Modeling Transmission Dynamics of COVID-19 in Nepal

A novel coronavirus disease (COVID-19) is an infectious viral disease caused by SARS-CoV-2. The disease was first reported in Wuhan, China, in December 2019, and it has been epidemic in more than 110 countries. The first case of COVID-19 was found in Nepal on 23 January, 2020. Now the number of confirmed cases is increasing day by day. Thus, the disease has become a ma-jor public health concern in Nepal. The propose of this study is to describe the development of outbreak of the disease and to predict the outbreak in Nepal. In the present work, the transmission dynamics of the disease in Nepal is analyzed mathematically with the help of SIR compartmental model. Reported data from June 1 st to June 17 th 2020 of Nepal are used to identify the model parameters. The basic reproduction number of COVID-19 outbreak in Nepal is estimated. Predictions of the peak epidemic time and the final size of the epidemic are made using the model. Our work predicts that, after 125 days from June 1 the infection will reach the peak. In this work, a good corre-lation between the reported data and the estimation given by our model is observed.


Introduction
COVID-19 was first reported in December 2019 in Wuhan city of China, and later it also became rapidly epidemic in other countries. On 17 June 2020, more than 8.4 million cases have been reported from more than 110 countries and territories. More than 452 thousand deaths and more than 4.24 million people have recovered [1]. The latest data of COVID-19 cases show that the cases are increasing rapidly in Nepal.
The first imported case of coronavirus was reported in Nepal on 23 January 2020, from a person traveling from Wuhan, China [2] [3]. There are total 7177 infected people in Nepal from 73 districts out of 77 district on 17 th June, 2020; age ranged from 2-month infants to 81-year-old women [3]. Government of Nepal announced country-wide lockdown from 24 March to 21 July to control the disease.  [12] have been proposed to predict future COVID-19 cases, to study its transmission dynamics, and so on. Y. Souleiman et al. predicted the outbreak of COVID-19 in Djibouti with the help of mathematical model [13]. Y.
Tang and S. Wang investigated the outbreak of COVID-19 in US [10].
In the present work, a simple epidemic SIR model is taken to track the outbreaks of COVID-19 in Nepal. At first we estimate some model parameters from the data provided by the Government of Nepal and we define the basic reproduction number. Then, using estimated parameters in the model we identify the peak of the outbreak and predict the infected population at the end of infection when no control efforts are implemented. The sources of COVID-19 cases data are taken from [3].
The outbreak of COVID-19 in Nepal has gone through different phases. In the beginning of the first week of May, the total cumulated cases were less than 100.
In the last week, the total number of reported cases was increased to over 1000 and the number went up in June continuously and reached 7177 reported positive cases on June 17. Therefore, our modeling work started from 1 st June.

Data
The study is based on the daily reported cases extracted from the Ministry of Health and Population of Nepal [3]. The data contains suspected cases, new confirmed cases, cumulative confirmed cases, recovered cases, and death cases due to COVID-19 infection ( Figure 1). From the first week of June, new confirmed cases have been more than 200. Thus, we choose June 1 st to June 17 th 2020 as the observation date and use the daily reported cumulative and new conform cases ( Figure 2).

Model Formulation
For the formulation of the model, the total population at time t is denoted by ( ) N t , it is subdivided into three compartments: Susceptible: ( ) S t , Infected: It is assumed that there is no birth, no immigration, and recovery from the disease confers immunity against the disease. Also there is a fixed infection rate per day and a fixed recovery time. People are well mixed. Journal of Applied Mathematics and Physics

Result
In this section, we use the model (1) to fit the cumulative infectious cases from June 1 st to June 17 th , 2020 in Nepal. Through some rational assumptions and parameter estimations, the fitting curves of cumulative cases using model (1) are shown in Figure 4. The simulation of the model is made by numerical solution applying Runge Kutta method of order 4. The figure indicates that our model provides a well fit to the reported data from June 1 st to June 17 th 2020 in Nepal. Figure 4 shows that the disease will grow rapidly in the coming days until it reached to the peak and end of June, there will be about 20,000 infected population in Nepal. Journal of Applied Mathematics and Physics  The result shows that the infection will reach at the peak after 125 days from June 1 st 2020 (From Figure 3). Effective control measures such as social distancing, self-isolation, disease testing facilities, face mask wearing, related policies etc. are helpful in the control of the disease.