Effects of Nonmonotonic Functional Responses on a Disease Transmission Model: Modeling and Simulation

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Epidemic modeling is crucial for understanding disease transmission.
• Nonmonotonic incidence and treatment rates can significantly alter disease dynamics.
• Previous models often assume simpler, monotonic relationships.

Purpose of the Study:

• To propose and mathematically analyze a novel Susceptible-Infected-Recovered (SIR) epidemic model.
• To incorporate nonmonotonic incidence and treatment rates using the Monod-Haldane functional response.
• To investigate the stability of disease-free and endemic equilibria.

Main Methods:

• Mathematical modeling of epidemic dynamics.
• Analysis of equilibrium points and their stability (local and global).
• Bifurcation analysis to understand transitions in model behavior.
• Numerical simulations to validate theoretical findings.

Main Results:

• The model exhibits two equilibria: a disease-free equilibrium (DFE) and an endemic equilibrium (EE).
• The basic reproduction number determines the local stability of the DFE.
• Conditions for the existence and local stability of the EE were identified.
• Global stability of both equilibria was investigated.

Conclusions:

• The proposed model provides a more realistic framework for studying epidemic dynamics with complex rate functions.
• The stability analysis offers insights into disease persistence and eradication.
• Numerical simulations confirm the theoretical predictions regarding model behavior.