Key result
Delayed SIRV model shows basic reproduction number determines FMD threshold dynamics and potential Hopf bifurcation.
Why the study?
Foot-and-mouth disease is a highly contagious viral disease in cloven-hoofed animals causing significant economic losses, requiring models to reveal its transmission dynamics.
This mathematical model demonstrates how age structure and time delay affect the transmission dynamics of foot-and-mouth disease.
Foot‐and‐mouth disease (FMD) is a highly contagious viral disease affecting cloven‐hoofed animals, causing significant economic losses and posing a major global concern for livestock industries. In order to reveal the transmission dynamics of FMD, this paper formulates a novel FMD model with age structure for immunologically recovered animals and a time delay. The time delay occurs in the transition from immune to recovered animals. By reformulating the model as an abstract Cauchy problem, we demonstrate the existence of equilibria. The basic reproduction number determines the FMD model's threshold dynamics: the virus‐free equilibrium is globally asymptotically stable when . When , the endemic equilibrium becomes unstable, indicating potential Hopf bifurcation. Numerical simulations support these findings and highlight how main system parameters affect FMD transmission.
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Yan et al. (2026) studied Foot-and-Mouth Disease (FMD). Mathematical modeling was evaluated on Threshold dynamics and stability of equilibria. A delayed SIRV model for Foot-and-Mouth Disease demonstrated that the basic reproduction number determines threshold dynamics, with potential Hopf bifurcation when the endemic equilibrium is unstable.
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