A Structured Avian Influenza Model with Imperfect Vaccination and Vaccine-Induced Asymptomatic Infection

Abstract

We introduce a model of avian influenza in domestic birds with imperfect vaccination and age-since-vaccination structure. The model has four components: susceptible birds, vaccinated birds (stratified by vaccination age), asymptomatically infected birds, and infected birds. The model includes reduction in the probability of infection, decreasing severity of disease of vaccinated birds and vaccine waning. The basic reproduction number, $\mathcal R_0$, is calculated. The disease-free equilibrium is found to be globally stable under certain conditions when ${\mathcal {R}}_0<1$. When ${\mathcal {R}}_0>1$, existence of an endemic equilibrium is proved (with uniqueness for the ODE case and local stability under stricter conditions) and uniform persistence of the disease is established. The inclusion of reduction in susceptibility of vaccinated birds, reduction in infectiousness of asymptomatically infected birds and vaccine waning can have important implications for disease control. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected, resulting in the “silent spread” of the disease. We also study the effects of vaccine efficacy on disease prevalence and the minimum critical vaccination coverage, a threshold value for vaccination coverage to avoid an increase in total disease prevalence due to asymptomatic infection.