Stability Analysis and Real-Data Validation of a Delayed Monkeypox Epidemic Model With Saturated Incidence

The current research examines the stability characteristics and practical uses of a delayed monkeypox outbreak model. The model divides the human population into four compartments: susceptible, exposed, infectious, and recovered individuals. A discrete time delay is incorporated to represent the incubation period and public-health response. The model uses a saturated incidence rate to show how people change their behavior when there are high infection rates. The study derives the disease-free and endemic equilibria while it calculates the basic reproduction number through the next-generation method. The research establishes solution positivity and solution boundedness while it uses the Routh–Hurwitz criterion and Lyapunov function techniques to study local and global system stability. The most important parameters which control disease transmission were found through sensitivity analysis. The model parameters were determined through analysis of actual outbreak data from the 2022 mpox outbreak in Portugal. The numerical simulations demonstrate that increasing the delay parameter leads to a decrease in peak infected individuals while it shifts the system toward disease-free equilibrium which has a major effect on transmission patterns throughout an extended time period.