Mathematical modeling and analysis of the transmission dynamics of novel Corona virous (Covid-۱۹) pandemic disease

In this paper, we have formulated a deterministic mathematical model of the novel corona virus to describe the dynamics of virus transmission in the community using a system of nonlinear ordinary differential equations. The invariant region of the solution, conditions for the positivity of the solution,  existence of equilibrium points and their stabilities analysis, sensitivity analysis and numerical simulation of the model were determined. The system of a model equation has two equilibrium points, namely the disease-free equilibrium points where the disease does not exist and the endemic equilibrium points where the disease persists.  Both local and global stability of the disease-free equilibrium and endemic equilibrium points of the model equation were established. The basic reproduction number that represents the epidemic indicator was obtained by using a next-generation matrix. The endemic states were considered to exist when the basic reproduction number was greater than one. Finally, our numerical findings were illustrated through computer simulations using MATLAB R۲۰۱۵b with ode۴۵ solver which shows the reliability of our model from the practical point of view. From our simulation results of the model, we came to realize that the number of infected people keeps decreasing if one carefully decreases the effective contact rate among protected and infectious individuals.

Keywords:

Analysis , COVID-۱۹ , Model , reproduction number , stability