The global outbreak of the monkeypox virus (Mpox) in 2022–2023, which affected over 100 countries, has underscored the urgent need for robust public health interventions and predictive modeling tools. In this study, we develop a novel mathematical model that captures the transmission dynamics of Mpox between human and rodent populations, incorporating both direct and environmental transmission pathways as well as the effects of vaccination. We prove the model's positivity and boundedness to ensure epidemiological feasibility. Using the next-generation matrix method, we derive the basic reproduction number and assess the local and global stability of both disease-free and endemic equilibria through Lyapunov-based techniques. Sensitivity analysis identifies critical parameters influencing Mpox spread and informs targeted intervention strategies. Numerical simulations illustrate how varying key parameters such as vaccination rates, recovery rates, and transmission pathways affect disease progression. The results emphasize that increasing vaccination coverage and enhancing recovery rates can significantly reduce disease burden. This model provides a comprehensive framework to support evidence-based public health decision-making for controlling future Mpox outbreaks.

Dengue impacts 129 nations, threatens over 50% of the global population, and results in around 400 million illnesses annually. The purpose of this paper was to build the global stability and sensitivity analysis of a vector-host dengue mathematical model with compartments of symptomatic and hospitalized infected humans. Additionally, it aimed to assess the impact of the immunological response of vulnerable individuals, through the ingestion of natural foods, on the transmission of the disease. The solution's positivity and boundedness proved the model's mathematical well-posedness. To examine endemicity, the reproduction number was calculated using the next-generation technique. The Lyapunov function approach was employed to illustrate the model's global stability. Our mathematical discoveries were illustrated through numerical simulations of the dengue epidemic. The dynamical system sensitivity analysis suggests that the best way to control illness is to increase the immune system rate of susceptible hosts by consuming natural foods.