Modeling on cost-effectiveness of monkeypox disease control strategies with consideration of environmental transmission effects in the presence of vaccination

Monkeypox (Mpox) is a viral disease caused by Mpox virus. The virus is transmitted through direct contact with an infected animal or human. This disease is now a global emergency triggered by rodents and contaminated surfaces. We propose a deterministic mathematical model which incorporates the direct transmission and the indirect transmission of the disease from the environment. For the model analysis, the threshold parameter called a basic reproduction number denoted by R 0 is calculated. Four time dependent control variables: vaccination, isolation, disinfection of the environment, and culling of infected animals are applied to the model. A qualitative analysis of the model is carried out to investigate the long term effect of the disease on the host populations. Moreover, global sensitivity analysis is conducted to identify statistically significant parameters to the system dynamics. The sensitivity analysis revealed that the dynamics of total infection count in humans and animals are negatively and persistently impacted by the removal rate of infected animals. Therefore, interventions that increase the removal rate of infected animals reduce the total number of infections. Furthermore, it is shown that at an early stage of the disease dynamics, the rate of disease transmission from an Mpox-contaminated environment to susceptible humans and animals is statistically significant in determining the numbers of infected humans. The Pontryagin’s Maximum Principle is used to derive the necessary conditions for the optimal control problem to the disease transmission dynamics. Incremental Cost-Effectiveness Ratio is calculated to investigate the cost-effectiveness of all the possible control strategies. The study found that vaccination, disinfecting the environment, and culling infected animals are the most effective ways to control the disease. By the end of the intervention period, this cost-effective control strategy averts the infection of about 255 animal and 2, 358 human populations. Therefore, in order to effectively control the Mpox outbreak, this article recommends that public health practitioners and the community in general should apply the combination of vaccination, environmental cleaning and disinfecting as well as removing infected animals in a higher proportion.