Controlling Chaotic Outbreaks In A Discrete Epidemic Model With Vaccination And Quarantine Interventions And Limited Medical Resources Using A Human-Based Metaheuristics Algorithm

Abstract

Infectious diseases can spread rapidly and develop into epidemics. This process can be analyzed using a simple model known as a discrete dynamic system. In this model, several important factors can be considered, such as vaccination, quarantine measures, and limited medical resources. Understanding the role of these factors in either preventing or worsening an outbreak can be improved by analyzing how each one influences the spread of disease. This study builds an epidemiological model that includes all three factors. The analysis focuses on system stability, the possibility of sudden changes in behavior (bifurcation), and the emergence of unpredictable patterns (chaos). Numerical simulations are used to examine how each factor affects disease transmission. In addition, efforts are made to control the chaotic behavior observed in the system. Limited medical resources are known to trigger spikes in case numbers. Vaccination plays a key role in addressing this issue, both by improving effectiveness and ensuring better distribution across the population. The model shows that higher infection rates can lead to chaotic behavior, making epidemic control more challenging. One approach to reducing chaos is by directly lowering the rate at which the disease spreads. A metaheuristic method is used to find the most effective control values for managing the spread of disease. This method helps minimize the gap between the expected results and the actual chaotic behavior of the system during simulations. The findings show that this approach is effective in guiding the system from a chaotic state toward a more stable condition. These results are consistent with the general principles of the OGY method, demonstrating that the improved version can successfully control chaotic behavior in the system. Keywords: Nonlinear Dynamics, Bifurcation, Disease Management, Public Health Policy, Metaheuristic Optimization of OGY Parameters