Dynamics analysis of an SVEIR epidemic model in a patchy environment

Area of Science:

• Mathematical modeling
• Epidemiology
• Public health

Background:

• Understanding disease dynamics is crucial for effective public health interventions.
• Previous models often do not account for multi-patch populations and comprehensive vaccination strategies.

Purpose of the Study:

• To develop and analyze a multi-patch SVEIR (Susceptible-Vaccinated-Infected-Exposed-Recovered) epidemic model.
• To investigate the impact of vaccinating both newborns and susceptible individuals.
• To assess the influence of population migration on disease transmission.

Main Methods:

• Formulation of a compartmental SVEIR model with distinct patches.
• Calculation of the basic reproduction number ($R_0$).
• Analysis of the stability of the disease-free equilibrium ($P_0$).
• Numerical simulations to explore disease spread and control.

Main Results:

• The disease-free equilibrium is stable when $R_0 < 1$ and unstable when $R_0 > 1$.
• The disease is uniformly persistent in the population if $R_0 > 1$.
• Vaccination strategies demonstrated effectiveness in controlling disease spread across all patches.
• Population migration was shown to potentially intensify or mitigate disease transmission within patches.

Conclusions:

• The proposed SVEIR model provides insights into multi-patch epidemic dynamics.
• Vaccination is a key strategy for controlling infectious diseases in interconnected populations.
• Migration patterns significantly influence the effectiveness of control measures and disease persistence.