Global stability and bifurcation of a COVID-19 virus modeling with possible loss of the immunity

Abstract

The present paper describes the mathematical model to investigate current covid-19 outbreak through close contact between infected people and other people but sometimes the infected people could show two cases; the first is symptomatic and the other is asymptomatic (carrier) as the source of the risk. Due to transmission characteristics of COVID-19, we can divide the individuals into 4 classes; 1st one describe the individuals that susceptible, 2nd one refers to carrier individuals (asymptomatic), 3rd one is infected ones and the 4th one is individuals that recovered. Model solutions for uniqueness, boundless and existence are discussed. Determination for all possible model equilibrium points was done. R as number for basic reproduction was utilized for model stability; if R0 < 1 the virus free equilibrium is locally stable asymptotically, but if R0 >1 the endemic equilibrium is locally stable asymptotically. Further, we conduct a detailed analysis of this model numerically by presenting many graphical results and detect the influence of parameters variation of how the disease spreads. our result indicate that the effect corona virus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.