Analyzing Global Stability of M-Pox Disease Dynamics: Mathematical Insights into Detection and Treatment Strategies

Abstract

In this research, a mathematical model is constructed to scrutinize the transmission patterns of monkeypox (mpox), with a specific emphasis on integrating the early detection of infected undetected individuals to curb its transmission. This research takes into account a range of factors influencing the propagation of monkeypox, encompassing population demographics, contact dynamics, and the efficacy of early detection of unidentified infected individuals. Employing the next-generation matrix method, the basic reproduction number (R0) is computed, revealing that the disease-free equilibrium state is locally asymptotically stable when (R0<1). This suggests that containment of monkeypox is achievable within a human populace where (R0) remains below one (1), yet it transitions to an endemic state when (R0) exceeds this critical value one (1). Furthermore, a sensitivity analysis is conducted to evaluate the robustness of our findings to variations in model parameters. Utilizing numerical simulations conducted via MAPLE 18, we demonstrate the significance of prompt identification and immediate intervention for infected individuals who may otherwise go undetected, in effectively diminishing the dynamic propagation of monkeypox. The results underscore the pivotal role of early detection in mitigating monkeypox outbreaks and curtailing transmission rates.