A generalized model of intra-host CHIKV infection with two routes of infection has been proposed. In a first step, the basic reproduction number \(\mathscr {R}_0\) 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 \(\bar{E}\) is globally asymptotically stable when \(\mathscr {R}_0\le 1,\) and the infected steady state \(E^*\) is globally asymptotically stable when \(\mathscr {R}_0>1\). 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.

已经提出了具有两种感染途径的宿主内 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\(\mathscr {R}_0\)，并使用李雅普诺夫方法进行稳态的局部和全局稳定性分析。证明当\(\mathscr {R}_0\le 1,\)和感染稳态\(E^*\)时，无CHIKV稳态\(\bar{E}\)是全局渐近稳定的当\(\mathscr {R}_0>1\)时全局渐近稳定. 在第二步中，我们通过抗体的流速应用了最佳策略，以优化受感染的隔室并最大化未感染的隔室。为此，我们制定了一个非线性最优控制问题。使用伴随变量讨论和表征了最优解的存在。因此，应用基于竞争性高斯-赛德尔隐式差分方法的算法来解决最优系统。一些数值模拟证实了理论结果。