Control Strategies for a Multi-strain Epidemic Model

This article studies a multi-strain epidemic model with diffusion and environmental heterogeneity. We address the question of a control strategy for multiple strains of the infectious disease by investigating how the local distributions of the transmission and recovery rates affect the dynamics of the disease. Our study covers both full model (in which case the diffusion rates for all subgroups of the population are positive) and the ODE-PDE case (in which case we require a total lock-down of the susceptible subgroup and allow the infected subgroups to have positive diffusion rates). In each case, a basic reproduction number of the epidemic model is defined and it is shown that if this reproduction number is less than one then the disease will be eradicated in the long run. On the other hand, if the reproduction number is greater than one, then the disease will become permanent. Moreover, we show that when the disease is permanent, creating a common safety area against all strains and lowering the diffusion rate of the susceptible subgroup will result in reducing the number of infected populations. Numerical simulations are presented to support our theoretical findings.

Automated summary

This article studies a multi-strain epidemic model with diffusion and environmental heterogeneity and investigates the control strategy for multiple strains of infectious disease. It is shown that the dynamics of the disease are affected by the local distributions of transmission and recovery rates. The basic reproduction number of the epidemic model is defined and used to determine the long-term outcome of the disease. The article also suggests that reducing the diffusion rate of the susceptible population and creating a common safety area can help reduce the number of infected individuals.