Within-Host Model of Dengue Viral Infection with Immune Response and Vaccination: Dynamics Analysis and Optimal Control
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Abstract
In this study, we propose a within-host model describing dengue viral infection. The model incorporates immune response and latency stage of cells when getting infected by dengue viruses. We verify that all solutions are nonnegative and bounded. Two equilibrium points (infection-free and infected) are established, and the basic reproduction number is computed. Local stability analysis is performed and each equilibrium point is stable under some conditions. The Lyapunov functional and geometric approaches are implemented to show the global stability of infection-free and infected equilibrium point, respectively. Numerical simulation of the model is carried out to confirm the stability of both equilibrium points i.e., the case when the basic reproduction number is less than and greater than one, respectively. Further, an optimal control problem is applied into the model by adding vaccination as control variable to seek the optimal strategy in preventing dengue viral infection. Our numerical results of optimal control model demonstrate that vaccination not only reduces exposed and infected cells, viruses, B-cells and cytotoxic T lymphocytes (CTLs), but also increases antibody. Our results indicate that vaccination can delay the peak of infection, potentially mitigating disease spread. Although most of the dengue patients are not in severe case, it is still better not to get infected and being risk. Therefore, dengue vaccination measure is highly recommended for public health policy in order to reduce both number of dengue infected patients and cost of treatment.
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