Long-term behavior of stochastic SIQRS epidemic models

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• SIQRS models track disease spread through Susceptible, Infected, Quarantined, and Recovered populations.
• Existing models often lack realistic random environmental changes and reinfection dynamics.

Purpose of the Study:

• To analyze and classify the dynamics of SIQRS epidemiological models with general incidence.
• To incorporate two types of random fluctuations: parameter variations (white noise) and environmental regime shifts.
• To determine the long-term disease fate based on a critical threshold value.

Main Methods:

• Stochastic differential equations to model random fluctuations.
• Analysis of a real-valued threshold parameter ($$) governing disease persistence.
• Explicit computation of the threshold for specific model examples.
• Simulation of model dynamics to illustrate real-world scenarios.

Main Results:

• The long-term disease behavior is dictated by the threshold $$.
• If $$, the disease asymptotically goes extinct at an exponential rate.
• If $$, the disease persists indefinitely.

Conclusions:

• The study provides a robust framework for understanding disease dynamics under realistic random conditions.
• The identified threshold offers a critical indicator for disease control and eradication strategies.
• Findings are applicable to various infectious diseases, including those with reinfection potential.