Optimal control analysis of Monkeypox disease with the impact of environmental transmission

Monkeypox is an emerging zoonotic viral disease resembling that of smallpox, although it is clinically less severe. Following the COVID-19 outbreak, monkeypox is an additional global health concern. The present study aims to formulate a novel mathematical model to examine various epidemiological aspects and to suggest optimized control strategies for the ongoing outbreak. The environmental viral concentration plays an important role in disease incidence. Therefore, in this study, we consider the impact of the environmental viral concentration on disease dynamics and control. The model is first constructed with constant control measures.The basic mathematical properties including equilibria, stability, and reproduction number of the monkeypox model are presented. Furthermore, using the nonlinear least square method, we estimate the model parameters from the actual cases reported in the USA during a recent outbreak in 2022. Normalized sensitivity analysis is performed to develop the optimal control problem. Based on the sensitivity indices of the model parameters, the model is reformulated by introducing six control variables. Based on theoretical and simulation results, we conclude that considering all suggested control measures simultaneously is the effective and optimal strategy to curtail the infection. We believe that the outcomes of this study will be helpful in understanding the dynamics and prevention of upcoming monkeypox outbreaks.