A Seiv Vaccination Model with General Non-Linear Incidence Rate and Waning Preventive Vaccine

Abstract

This study adopted and analyzed a SEIV (Susceptible, Exposed, Infected, and Vaccinated) vaccination model with general non-linear incidence rate and waning preventive vaccine. Thereafter the Basic Reproduction Number of the disease free equilibrium was found and simulated, it was found to be globally asymptotically stable. The epidemic free equilibrium was also found, analyzed using the Bellman and Cooke's Theorem. The result of the analyses was simulated using MATLAB and found that it is Stable on probability points of the vaccine waning period from 1.0 down to 0.3 and unstable on the points 0.2 and 0.1. Which is logical, that is, as the vaccine efficacy decreases so does the stability of the model.