Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Epidemic models are crucial for understanding disease spread.
• Virus mutation can alter disease dynamics and persistence.
• Non-monotone incidence rates add complexity to epidemic modeling.

Purpose of the Study:

• To investigate a diffusive two-strain epidemic model incorporating non-monotone incidence and virus mutation.
• To analyze the existence, boundedness, and stability of equilibrium points.
• To determine the conditions under which each strain can persist in the population.

Main Methods:

• Development of a diffusive two-strain epidemic model.
• Analysis of the positivity, existence, and uniform boundedness of solutions.
• Application of Lyapunov functionals for global asymptotic stability analysis of equilibrium points.

Main Results:

• The model exhibits three equilibrium points: infection-free, strain-2 endemic, and co-infection (both strains) endemic.
• A strain-1 endemic equilibrium point does not exist, likely due to virus mutation.
• The analysis provides insights into the conditions for disease persistence.

Conclusions:

• Virus mutation can prevent the persistence of a specific strain (strain-1) in the community.
• The model demonstrates that co-infection dynamics are possible even when one strain cannot persist.
• Mathematical modeling is essential for predicting epidemiological outcomes under complex scenarios like virus mutation.