Department of Mathematics, University of Florida, Gainesville, USA.
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, USA.
Bull Math Biol. 2021 Jan 16;83(3):18. doi: 10.1007/s11538-020-00855-3.
In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number [Formula: see text] of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when [Formula: see text] and unstable when [Formula: see text]. Numerical simulations suggest that [Formula: see text] increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes.
在本文中，我们构建了一个 HIV 多尺度嵌套免疫流行病学模型，该模型建立在复杂网络之上。系统由常微分方程与偏微分方程耦合而成。首先，我们证明了免疫模型的存在性和唯一性，然后建立了多尺度模型的适定性。我们推导出了免疫流行病学模型的基本再生数[Formula: see text]的显式表达式。系统存在无病平衡点和地方病平衡点。当[Formula: see text]时，无病平衡点全局稳定，当[Formula: see text]时不稳定。数值模拟表明，当网络中的节点数增加时，[Formula: see text]增加。此外，我们发现对于无标度网络，平衡点处的感染个体数是宿主内繁殖数的驼峰函数；然而，如果网络主要由低连通度节点或高连通度节点组成，则这种依赖性变为单调。
