Modeling Monkeypox: Spread of Outbreak with Social Distancing, Quarantine and Vaccination

In this paper, we introduced a novel mathematical model to simulate the spread of the zoonotic viral disease monkeypox, incorporating both human and rodent populations to capture the disease dynamics. Unlike previous models, we included a quarantine compartment for infected humans, a social distancing compartment for susceptible individuals, and vaccination with direct transmission to the recovered compartment, offering a more comprehensive framework for controlling the spread of monkeypox. We then compared the effectiveness of these three control measures in reducing disease transmission. To investigate the dynamics of the model, we first demonstrated that it has a unique, positive, and bounded solution. Next, we calculated the basic reproduction number, R_0 for the proposed model. A sensitivity analysis is then conducted to identify key parameters, followed by an assessment of their effects on R_0. Additionally, we analyzed the local stability of both the disease-free and endemic equilibrium points to identify the conditions under which the disease dies out or remains endemic. We first showed in stability analysis section that these three control parameters play important roles in stability of equlibrium points. After that our findings in sensitivity analysis indicated the critical role of recovery rates and incubation periods in shaping the outbreak trajectory. Besides them, our analysis of R_0 in 3-D plots showed that the human-to-human transmission (β_hh) has about 3 times greater impact than rodent-to-human transmission (β_rh) on R_0. Finally, we presented simulations to show single and combined effects of the control parameters: quarantine, social distancing and vaccination on the transmission of monkeypox virus.