Dynamics and control of foot-and-mouth disease in endemic countries: A pair approximation model
Various mathematical models have been developed to describe spatial farm-to-farm transmission of foot and mouth disease (FMD). These models have explored the impacts of control measures such as culling and vaccination during a single outbreak in a country normally free of FMD. As a result, these models do not include factors that are relevant to countries where FMD is endemic in some regions, like long-term waning natural and vaccine immunity, use of prophylactic vaccination, and disease re-importations. These factors may have implications for disease dynamics and control, and yet few mathematical models have been developed for FMD-endemic settings. Here we develop and study an SEIRV (susceptible-exposed-infectious-recovered-vaccinated) pair approximation model of FMD. We focus on long term dynamics by exploring characteristics of repeated outbreaks of FMD and their dependence on disease re-importation, loss of natural immunity, and vaccine waning. We find that prophylactic vaccination is more effective than ring vaccination, for the same per capita vaccination rate, but the effectiveness of any vaccination strategy strongly depends on duration of natural immunity, rate of vaccine waning, and disease re-introduction. Changing the duration of natural immunity generally has a more profound impact on the number and magnitudes of FMD outbreaks than changing the duration of vaccine immunity. If loss of natural immunity and/or vaccine waning happen rapidly, then large multiple subsequent outbreaks result, making it difficult to eliminate the disease. Finally, more frequent disease re-importations causes a higher cumulative number of infections, although a lower average epidemic peak. Because of the differences between dynamics in FMD-free settings versus FMD-endemic settings, and because FMD is a global problem, more mathematical models tailored to FMD-endemic countries should be developed that include factors like waning natural and vaccine immunity and the impact of repeated disease importations.