Mathematical modeling and analysis of a novel monkeypox virus spread integrating imperfect vaccination and nonlinear incidence rates

Abstract

In this paper, we introduce a novel model that simulates the spread of the monkeypox virus. The new model takes into account the effect of the interaction between the human and rodent population along with some realistic factors that have not been introduced before such as imperfect vaccination and nonlinear incidence rates. Moreover, the human population is further divided into low-risk and high-risk groups to better reflect recent observations. To understand the dynamics of the new model, the existence, uniqueness, and continuous dependence on initial conditions, as well as its positivity and boundedness of the model are investigated in detail. The obtained solution is proved to be positive and has bounded behavior. Furthermore, the reproduction number R0 for the proposed system is computed and detailed bifurcation analysis is performed to reveal major qualitative changes in the model's dynamics. In addition, we investigate the influence of key parameters on the basic reproduction number. We also explore and analyze the stability of equilibrium points in the space of parameters. The new findings reveal that the virus is more frequently witnessed among the high-risk group, which may provide some restrictions to stop the spread through social limitations. To validate our theoretical results, we conduct numerical simulations, which provide insights into the behavior of the model under different conditions. The new findings aim in developing preventive control measures to suppress the spread of the virus and to develop effective strategies for controlling and preventing outbreaks, ultimately protecting public health and minimizing the impact of the disease.