Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model

Abstract

In this article we propose a stochastic model to discuss the dynamics of novel corona virus disease. We formulate the model to study the long run behavior in varying population environment. For this purposes we divided the total human population into three epidemiological compartments: the susceptible, covid-19 infected, recovered and recovered along with one class of reservoir. The existence and uniqueness of the newly formulated model will be studied to show the well-possedness of the model. Moreover, we investigate the extinction analysis as well as the persistence analysis to find the disease extinction and disease persistence conditions. At the end we perform simulation to justify the investigation of analytical work with the help of graphical representations.

Keywords: COVID-19; Existence and uniqueness analysis; Extinction as well as persistence; Simulation; Stochastic model.

Fig. 1

The dynamics of the novel corona virus model (1) against the relative parameters as stated above and initial sizes of compartmental populations $\left(s\right(0)=0.9,i(0)=0.7,r(0)=0.5,w(0)=0.3)$.