The behaviour of measles transmission in three different populations

Abstract

SIR Model can be employed to model the transmission of either fatal or non-fatal disease within a closed population based on certain assumptions. In this paper, the behaviour of non-fatal diseases transmission model is observed from three types of population, that is (i) increasing population, (ii) constant population, (iii) decreasing population. This paper acquired two equilibria, i.e, the disease-free equilibrium point (μμS,0,0) and the endemic equilibrium point (α+μIβ,μβ-μSα-μSμIβ(α+μI),α(μβ-μSα-μSμI)β(α+μI)μR) . At the disease-free equilibrium, the behaviour of the model is stable when β<μSμ(μI+α) , while at the endemic equilibrium, its behaviour is stable for any positive parameters α, β, μ, μS, μI, and μR.