MODELING THE DYNAMICS OF DIPHTHERIA WITH PUBLIC AWARENESS

Abstract

Diphtheria is a highly contagious bacterial infection that primarily affects the mucous membranes  of the nose, throat, and airways. It is caused by the bacterium Corynebacterium diphtheriae, which produces a toxin that damages the respiratory system, heart, and nervous system. Despite  the existence of effective vaccines, diphtheria continues to pose a threat to global health. In this paper, we developed a nonlinear deterministic model which incorporates public awareness and  isolation to describe the dynamics of diphtheria. Analysis of the model reveals that the boundedness and positivity of solutions have been ascertained, diphtheria free equilibrium is both locally and globally asymptotically stable whenever the associated control reproduction number Rc < 1 and unstable when Rc > 1, similarly the endemic equilibrium is globally asymptotically stable when the control reproduction Rc > 1 and ϕ = τ = δ1 = δ2 = 0. Moreover, the model undergoes backward bifurcation in which a stable disease-free equilibrium coexists with a stable endemic equilibrium. The epidemiological implication of backward bifurcation is Rc < 1 is necessary but not sufficient condition for control of diphtheria even when the classical requirement are satisfied. The most  sensitive parameters for the control of the spread of diphtheria are identified by forward sensitivity index method and found that contact rate β and progression rate of exposed individuals to infected compartment are the most sensitive parameters for increasing the transmission. On the contrary, isolation rate τ and recovery rate of infected individuals γ1 are the most sensitive for reducing the spread...