El Hajji Miled
Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi Arabia.
ENIT-LAMSIN, Tunis El Manar university, BP. 37, Tunis-Belvédère, 1002, Tunis, Tunisia.
Theory Biosci. 2021 Feb;140(1):27-44. doi: 10.1007/s12064-020-00324-4. Epub 2020 Oct 31.
A generalized model of intra-host CHIKV infection with two routes of infection has been proposed. In a first step, the basic reproduction number [Formula: see text] was calculated using the next-generation matrix method and the local and global stability analyses of the steady states are carried out using the Lyapunov method. It is proven that the CHIKV-free steady state [Formula: see text] is globally asymptotically stable when [Formula: see text] and the infected steady state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy via the antibodies' flow rate in order to optimize infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using an adjoint variables. Thus, an algorithm based on competitive Gauss-Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.
已经提出了一种具有两种感染途径的宿主内基孔肯雅病毒（CHIKV）感染的广义模型。第一步，使用下一代矩阵方法计算基本再生数[公式：见原文]，并使用李雅普诺夫方法对稳态进行局部和全局稳定性分析。证明了当[公式：见原文]时，无CHIKV稳态[公式：见原文]是全局渐近稳定的，而当[公式：见原文]时，感染稳态[公式：见原文]是全局渐近稳定的。第二步，我们通过抗体流速应用一种最优策略，以优化感染区室并使未感染区室最大化。为此，我们制定了一个非线性最优控制问题。使用伴随变量讨论并刻画了最优解的存在性。因此，应用了一种基于竞争型高斯 - 赛德尔类隐式差分方法的算法来求解最优性系统。一些数值模拟证实了理论结果。
