Optimal control and cost-effectiveness analysis of mitigation strategies for monkeypox virus infection in the presence of routine interventions

Empirical evidence substantiates the pivotal role of vaccination in eradicating monkeypox virus (Mpox) infections. Mathematical modeling serves as a crucial tool for identifying strategies to curtail the disease’s proliferation. This study introduces a comprehensive mathematical framework for analyzing the dynamics of monkeypox transmission, incorporating imperfect vaccination and immunity degradation post-recovery. The theoretical constructs of positivity and boundedness are employed to confirm the model’s well-posedness. The next-generation matrix approach is utilized to calculate the control reproduction number (ℛ _c ), and the equilibrium points of the model are identified. The investigation demonstrates that the disease-free equilibrium is both locally and globally asymptotically stable, while the endemic equilibrium is proven to exhibit global asymptotic stability as well. Sensitivity analyses of parameters influencing ℛ _c are performed using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC). Furthermore, the model is extended to incorporate time-dependent interventions, including the administration of high-efficacy vaccines, the quarantine of exposed individuals, and the treatment of infected individuals. The model’s qualitative findings are reinforced through numerical simulations, which validate the effectiveness of various control strategies in suppressing monkeypox spread among susceptible, exposed, and infected populations. Simulations without vaccination controls reveal an initial surge in exposed and infected cases, followed by gradual containment over time. The findings highlight the critical importance of vaccination as a pharmaceutical intervention, though its effectiveness is hindered by challenges such as viral mutations, the diminishing efficacy of vaccines, and limited vaccination resources. These constraints underscore the necessity of adopting integrated intervention measures, especially as instances of reinfection post-vaccination and treatment of infected cases have been documented in several studies. Policymakers are thus encouraged to employ a balanced and pragmatic approach when easing other preventive measures for monkeypox. Additionally, a cost-effectiveness analysis was performed to determine the most economical strategy for controlling monkeypox transmission. The results indicate that the optimal control strategy involves combining high-efficacy vaccination with the quarantine of exposed individuals, demonstrating superior cost-effectiveness among the examined interventions.