Graph Theoretic Technique to the Global Stability Analysis of the Discrete Age Structured SVEIR Model with Application to Ebola Virus Disease

Abstract

Discrete age structured models provide a better approach of discussing the spread of infectious diseases with infectivity, mortality and recovery being age dependent. Measures such as vaccination are carried out in discrete time or applied to individuals in certain age-groups. In the past Ebola Virus disease (EVD) outbreaks, infections in children under 5 years was associated with high mortality rates. In this work, a general discrete SVEIR epidemic model with age structure is formulated. The study establishes the existence of the endemic equilibrium and further shows that it is globally stable using the graph theoretic approach on the method of Lyapunov functions. The model is then applied to EVD dynamics to study the impact of vaccination on the age structured population. The numerical simulation of the discrete age case scenario demonstrates that vaccination of children under 5 years of age against EVD has a great impact in reducing their susceptibility because of the active immune system as compared to the older population who have a poor response to vaccine immunity. For the older population, vaccination is not very eective in reducing their susceptibility.