Smart Computing and Informatics pp 395-402 | Cite as
A SIR Epidemic Model with Primary Immunodeficiency
Abstract
In this paper, we construct a SIR epidemic model where a small number of the susceptible individuals have low immunity levels. We divide the susceptible population into two groups based on their immunity levels and apply the transmission rate for these two populations. We derive the basic reproduction number denoted by \(R_{0}\). We have two equilibria namely the disease-free and endemic equilibrium. We analyze the stability of the equilibrium points both locally and globally. Finally, we have simulated our model through MATLAB and have proved our theoretical results using numerical simulations. From the simulations, we observe that by decreasing the primary immunodeficiency, we can decrease the infection.
Keywords
Difference equations Disease-free and endemic equilibria SIR epidemic model Basic reproduction numberReferences
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