MATHEMATICAL MODELING AND SENSITIVITY ANALYSIS OF COVID-19

Abstract

Coronaviruses are a large family of viruses that cause illness ranging from the common cold to more severe diseases. In this study, Mathematical Modeling and Sensitivity Analysis of Covid-19 was studied. For this, we formulated and analyzed a deterministic mathematical model of six compartments and viral spread in the environment for the transmission dynamics of COVID-19 infection using a system of non-linear ordinary differential equations. These compartments are namely susceptible, exposed, infectious with timely diagnosis,infectious with delayed diagnosis , the hospitalized and Recovered population. We have divided the infected cases into two groups: infectious with timely diagnosis and infectious with delay diagnosis population. Existence and Uniqueness of solution was proved, positivity of the solution of the model is proved and Boundedness of the solution was checked. The system has two equilibrium points, namely the disease free equilibrium point and the endemic equilibrium point. The model under consideration was nonlinear so that it was linearized by special transformation rule. The estimated basic reproduction number, R0, for the proposed model is 3.53. Equilibrium points are shown to be globally stable.Local Sensitivity analysis of the basic reproductive number (R0) showed that the most sensitive parameter is the recruitment rate. Finally, numerical simulations of the model equations were carried out using MATLAB Software.