Optimal Control Dynamics: Multi-therapies with Dual Immune Response for Treatment of Dual Delayed HIV-HBV Infections

It has been of concern for the most appropriate control mechanism associated with the growing complexity of dual HIV-HBV infectivity. Moreso, the scientific ineptitude towards an articulated mathematical model for co-infection dynamics and accompanying methodological application of desired chemotherapies inform this present investigation. Therefore, the uniqueness of this present study is not only ascribed by the quantitative maximization of susceptible state components but opined to an insight into the epidemiological identifiability of dual HIV-HBV infection transmission routes and the methodological application of triple-dual control functions. Using ODEs, the model was formulated as a penultimate 7-Dimensional mathematical dynamic HIV-HBV model, which was then transformed to an optimal control problem, following the introduction of multi-therapies in the presence of dual adaptive immune system and time delay lags. Applying classical Pontryagin’s maximum principle, the system was analyzed, leading to the derivation of the model optimality system and uniqueness of the system. Specifically, following the dual role of the adaptive immune system, which culminated into triple-dual application of multi-therapies, the investigation was characterized by dual delayed HIV-HBV virions decays from infected double-lymphocytes in a biphasic manner, accompanied by more complex decay profiles of infectious dual HIV-HBV virions. The result further led to significant triphasic maximization of susceptible double-lymphocytes and dual adaptive immune system (cytotoxic T-lymphocytes and humeral immune response) achieved under minimal systemic cost. Therefore, the model is comparatively a monumental and intellectual accomplishment, worthy of emulation for related and future dual infectivity.