An Age-Structured Model for Tilapia Lake Virus Transmission in Freshwater with Vertical and Horizontal Transmission

Abstract

This paper proposes a mathematical model for Tilapia Lake Virus (TiLV) transmission in wild and farmed tilapias within freshwater. This model takes into account two routes of transmission: vertical and horizontal. This latter route integrates both the direct and indirect transmission. We define an explicit formula for the reproductive number R0 and show by means of the Fatou's Lemma that the disease free equilibrium is globally asymptotically stable when, R0 < 1. Furthermore, we find an explicit formula of the endemic equilibria and study its local stability as well as the uniform persistence of the disease when R0 > 1. Finally, a numerical scheme to solve the model is developed and some parameters of the model are estimated based on biological data. The numerical results illustrate the role of routes of transmission on the epidemic evolution.