Outbreak and control of Foot and Mouth Disease within and across adjacent districts—A mathematical perspective

Abstract

In this study, we formulate a mathematical model for Foot and Mouth Disease (FMD) within and across two adjacent districts and use it to calculate the impact and cost effectiveness of vaccination and/ or quarantine in controlling this infection. The basic properties of the model are established and reproduction numbers for single district and two adjacent districts obtained. Steady states are examined and found to be both locally and globally stable. The model is transformed into an optimal control problem by incorporating time dependent controls to obtain the best strategy in controlling FMD among the cattle population. From numerical simulations, simultaneous implementation of vaccination with movement restriction is the most effective strategy in control and eventual eradication of FMD from cattle population. Further more, sole implementation of movement restriction across two adjacent and simultaneously infected districts is found to be ineffective in controlling FMD. However, using Incremental Cost Effectiveness Ratio analysis, it was determined that sole implementation of vaccination in both district one and two upon an FMD outbreak is the most cost-effective strategy to control and eventually eradicate FMD.

Keywords

• Foot and Mouth Disease
• Vaccination
• Optimal control
• Incremental cost effectiveness ratio
• Equilibrium state