Modeling foot-and-mouth disease dynamics with immigrants and control in Tanzania

Abstract

Foot-and-Mouth Disease (FMD) remains a significant threat to livestock health and food security in Tanzania, driven by uncontrolled animal movement and limited control measures. This study develops a data-driven mathematical model to assess FMD transmission dynamics, explicitly incorporating infective immigrants and key epidemiological factors. The model employs a compartmental SEVIATR (Susceptible–Exposed–Vaccinated–Infective–Asymptomatic–Treated–Recovered) framework and computes the effective reproduction number ($R_e$) using the next-generation matrix method. Local and global stability of the disease-free equilibrium are established via the Routh–Hurwitz criterion and a Lyapunov function, respectively. Sensitivity analysis identifies the transmission rate and biosecurity effectiveness as the primary drivers of $R_e$. Numerical simulations reveal that infective immigrants significantly increase $R_e$, highlighting the importance of border control. Integrated interventions, including vaccination, movement restrictions, and enhanced biosecurity, are shown to reduce $R_e$ below the epidemic threshold. The model is validated with national surveillance data and achieves improved predictive performance by incorporating seasonal variation and time-series forecasting. This study provides novel, region-specific insights into FMD dynamics and informs policymakers on effective, integrated control strategies for endemic settings.