Fractional-order model for two-strain Monkeypox virus: Analytical and numerical insights with optimal control strategies

In this study, we explore the dynamics of a proposed fractional-order model for human-to-human infections with dual strain Monkeypox viruses (MPVs). In addition, a suggested optimal control measures are investigated to manage the disease outbreaks within the community, which helps achieving good health and well-being goal of Sustainable Development Goals (SDGs). First, a comprehensive analytical study of the model is introduced to examine its essential properties, including existence, uniqueness, non-negativity, and boundedness of solutions. The equilibrium points of the model are found and a thorough stability analysis is conducted for each steady state. The possible bifurcation scenarios, that can be exhibited by the model, are also explored. The basic reproduction number R₀ is computed and the impacts of key parameters are examined through detailed sensitivity analysis. Then, the time-dependent control variables are employed to formulate a fractional optimal control problem (FOCP) for the present model, where Pontryagin's maximum principle (PMP) is used to constitute the necessary optimality conditions (NOCs). Numerical experiments are carried out to validate theoretical findings and assess the biological implications of the applied control measures. The numerical results indicate that the proposed combination of control strategies can effectively minimize the infection control costs while effectively working towards eradicating the infection.