Kenne Cyrille, Zongo Pascal, Dorville René
Laboratoire LAMIA, Université des Antilles, Pointe-à-Pitre, Guadeloupe (FWI), France.
Department of Mathematics, University of Buea, Buea, Cameroon.
J Biol Dyn. 2022 Dec;16(1):98-116. doi: 10.1080/17513758.2022.2033860.
The goal of this paper is to investigate the influence of the waning immunity on the dynamics of Tilapia Lake Virus (TiLV) transmission in wild and farmed tilapia within freshwater. We formulate a model for which susceptible individuals can contract the disease in two ways: (i) direct mode caused by contact with infected individuals; (ii) indirect mode due to the presence of pathogenic agents in the water. We obtain an age-structured model which combines both age since infection and age since recovery. We derive an explicit formula for the reproductive number and show that the disease-free equilibrium is locally asymptotically stable when, . We discuss on the form of the waning immunity parameter and show numerically that a Hopf bifurcation may occur for suitable immunity parameter values, which means that there is a periodic solution around the endemic equilibrium when, .
本文的目标是研究免疫力下降对罗非鱼湖病毒（TiLV）在淡水野生和养殖罗非鱼中传播动态的影响。我们构建了一个模型，其中易感个体可通过两种方式感染疾病：（i）与感染个体接触导致的直接感染模式；（ii）由于水中存在病原体导致的间接感染模式。我们得到了一个年龄结构模型，该模型结合了感染后的年龄和康复后的年龄。我们推导出了繁殖数的显式公式，并表明当 时，无病平衡点是局部渐近稳定的。我们讨论了免疫力下降参数的形式，并通过数值模拟表明，对于合适的免疫参数值可能会发生霍普夫分岔，这意味着当 时，在地方病平衡点周围存在一个周期解。
