Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Reaction-diffusion models are crucial for understanding disease spread.
• Vertical transmission in epidemic models adds complexity.
• Non-monotone systems present unique challenges in analysis.

Purpose of the Study:

• To investigate the spreading speed of an SI epidemic model with vertical transmission.
• To determine the conditions for disease persistence and extinction.
• To analyze the impact of critical speed on epidemic dynamics.

Main Methods:

• Analysis of a non-monotone reaction-diffusion SI model.
• Mathematical proofs for convergence to disease-free equilibrium.
• Derivation of a critical speed for epidemic spread.

Main Results:

• If the basic reproduction number (R0) is less than or equal to 1, the disease-free equilibrium is reached.
• If R0 > 1, a critical speed (c*) exists.
• Speeds below c* lead to persistent disease; speeds at or above c* lead to extinction.

Conclusions:

• The spreading speed critically influences epidemic outcomes.
• Vertical transmission and model non-monotonicity affect disease dynamics.
• Numerical simulations confirm the theoretical findings on asymptotic behavior.