Mathematical analysis of monkeypox infection with optimal control analysis: A case study with a new outbreak in the United States

Monkeypox infection is a serious illness to human health, and its outbreak has been reported in many non-endemic regions. Various approaches have been implemented to explore the epidemiology, transmission patterns, and effective control of monkeypox. In this paper, we focus on the implementation of a mathematical modeling approach to study the dynamics of monkeypox infection with a case study of the United States, the most impacted country in 2022. The proposed mathematical model is initially constructed using a nonlinear system of differential equations with constant control measures. The human population is divided into four subgroups while the animal (non-human) population is divided into three subclasses. An extensive theoretical analysis of the proposed monkeypox model is presented including the stability of equilibria. Further, to make the present study more visible to the literature, a real data set of the cumulative confirmed cases of monkeypox in the United States from May to October 2022 is used to estimate the proposed model parameters. Some of the demographic parameters are estimated from the population of the United States. The most important biological parameter R0$$ {\mathcal{R}}_0 $$ of the problem is investigated theoretically as well as numerically based on the reported cases. The impact of various model parameters on the dynamics of state variables and R0$$ {\mathcal{R}}_0 $$ is shown graphically. Furthermore, we analyzed the impact of various model parameters on the basic reproduction number to explore the most influential intervention strategy to curb the infection. The most crucial components of the proposed system are identified and health officials are advised. Finally, using optimization theory, the most effective optimized preventive strategies are suggested to curtail the infection in a community. We believe that the present investigation will be helpful in understanding the dynamics and prevention of monkeypox infection.