Modeling the transmission dynamics and optimal control analysis of Mpox infection incorporating vaccination control strategy

Abstract In this study, a novel deterministic model for the transmission dynamics of Mpox, structured as a nonlinear autonomous system, is constructed from a 13-compartment epidemiological framework. The model incorporates eight human compartments, four animal compartments, and one representing the environmental pathogen load. We obtained the equilibrium points and the basic reproduction number ( $$\mathcal {R}_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> ) by applying the appropriate algebraic manipulations and the next-generation matrix method. A detailed qualitative analysis is carried out to examine the local and global asymptotic stability of the model’s equilibria. A global sensitivity analysis of the basic reproduction number is conducted by using the parameter estimates obtained by fitting the mathematical model to Mpox infection case data from Nigeria, the United States, and Ghana. Furthermore, the study extends to optimal control by incorporating seven time-dependent control interventions into the nonlinear autonomous dynamic model. Using Pontryagin’s Maximum Principle, we derived optimal control strategies that minimize both disease burden and intervention costs. This integrated method provides a strong mathematical foundation for comprehending Mpox epidemiology and informing evidence-based public health policy decisions.