A SIR Epidemic Model with Primary Immunodeficiency and Time Delay

Abstract

In this paper, we have proposed a SIR (Susceptible-Infected-Recovered) epidemic model incorporating Primary Immunodeficiency and distributed delays. We discretize the model using a variation of Backward Euler method. We divide the susceptible population into two groups based on their immunity levels and apply the transmission rate for these two populations. We derive a threshold value known as the basic reproduction number denoted by \(R_0\). We have two equilibria namely the disease free and endemic equilibrium. We analyze the global stability of the disease free and endemic equilibrium using Lyapunov functional techniques. Finally, We prove our theoretical results using numerical simulations through MATLAB.