Bifurcation and chaotic dynamics in a spatiotemporal epidemic model with delayed optimal control, stochastic process,...

Area of Science:

• Mathematical Biology
• Epidemiology
• Dynamical Systems

Background:

• Epidemic modeling is crucial for understanding disease spread.
• Beddington-DeAngelis incidence and Holling Type II treatment rates offer insights into population dynamics and resource limitations.
• Inhibitory behaviors and treatment facility constraints significantly impact disease transmission.

Purpose of the Study:

• To introduce and analyze a novel epidemic model with specific incidence and treatment rates.
• To investigate the stability, bifurcations, and chaotic dynamics of the proposed model.
• To explore the impact of time delays, optimal control strategies, stochasticity, and spatial patterns on disease transmission.

Main Methods:

• Analysis of model well-posedness, local and global stability, and co-dimension bifurcations (1 and 2).
• Incorporation of time delays, chaos theory, sensitivity analysis (PRCC, EFAST), and optimal control (Pontryagin's maximum principle).
• Development of a stochastic model using continuous-time Markov chains, branching process approximation, and noise-induced pattern formation.

Main Results:

• Demonstration of chaos and identification of conditions leading to chaotic dynamics and control.
• Analytical estimation of disease extinction probability and epidemic occurrence.
• Identification of Turing instability criteria and generation of noise-induced patterns.

Conclusions:

• The study provides a comprehensive analysis of epidemic dynamics using diverse modeling techniques.
• Model parameters were estimated using COVID-19 (Poland) and HIV/AIDS (India) data, with results validated by numerical simulations.
• The significance of inhibitory effects from susceptible and infected populations in disease dynamics is highlighted.