RESUMO
This paper proposes and analyzes an immune-structured population model of tilapia subject to Tilapia Lake Virus (TiLV) disease. The model incorporates within-host dynamics, used to describe the interaction between the pathogen, the immune system and the waning of immunity. Individuals infected with a low dose acquire a low immunity level and those infected with a high dose acquire a high level of immunity. Since individuals' immune status plays an important role in the spread of infectious diseases at the population level, the within-host dynamics are connected to the between-host dynamics in the population. We define an explicit formula for the reproductive number [Formula: see text] and show that the disease-free equilibrium is locally asymptotically stable when [Formula: see text], while it is unstable when [Formula: see text]. Furthermore, we prove that an endemic equilibrium exists. We also study the influence of the initial distribution of host resistance on the spread of the disease, and find that hosts' initial resistance plays a crucial role in the disease dynamics. This suggests that the genetic selection aiming to improve hosts' initial resistance to TiLV could help fight the disease. The results also point out the crucial role played by the inoculum size. We find that the higher the initial inoculum size, the faster the dynamics of infection. Moreover, if the initial inoculum size is below a certain threshold, it may not result in an outbreak at the between-host level. Finally, the model shows that there is a strong negative correlation between heterogeneity and the probability of pathogen invasion.
Assuntos
Doenças dos Peixes , Tilápia , Viroses , Humanos , Animais , Conceitos Matemáticos , ProbabilidadeRESUMO
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 [Formula: see text] and show by means of the Fatou's lemma that the disease-free equilibrium is globally asymptotically stable when [Formula: see text]. 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 [Formula: see text]. 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.