Dynamic modelling to explore persistence of disease in endemic settings using foot and mouth disease as an exemplar

Abstract

Foot and mouth disease (FMD) costs over $20bn annually in large part due to control costs and production losses. Endemic regions such as sub-Saharan Africa (SSA) are particularly badly affected. Pastoral livestock keepers experience near yearly outbreaks, but the factors which contribute to persistence remain poorly understood. While epidemiological studies in endemic settings have identified risk factors such as transhumance (the seasonal movement of livestock to find better grazing), and enable understanding of the contemporary state of the system they have yet to explain how infection persists in these regions. Key aspects of a system can be explored relatively quickly and cheaply using modelling. However, modelling of FMD is more common for disease-free settings focusing specifically on disease control – starting with and returning to a system free of disease. While disease control in endemic settings is the ultimate aim, this first requires a better understanding of the mechanisms underlying persistence. For this, models specific to endemic settings are required and must account for key differences compared to disease-free settings. In this project a suite of stochastic models was developed to explore dynamics of a highly infectious, directly transmitted pathogen such as FMD. The models developed explore persistence and infection dynamics across local and regional scales investigating the impact of different factors in pastoralist systems and the perceived persistence of disease from field observations. A within-herd model shows that infection cannot persist for longer than 3 months without reintroduction. Including persistently infectious individuals in the model has little impact on the overall infection of individuals within the herd. This strongly supports the idea reintroduction of the disease is required to give the repeated outbreaks that are characteristic of endemic settings. Although exploring persistence likely requires models that account for transmission between herds, understanding of herd-level infection characteristics can be gained from this within-herd model. In endemic settings natural immunity in animals following infection can result in herd immunity and protection against reinfection. The model indicates the mean duration of herd immunity following a large outbreak in a naïve population is 2 years. The duration of herd immunity depends on the susceptibility of the herd prior to the outbreak, the size of the outbreak and the turnover of the population. Accurately predicting the dynamics of heterogeneous real-world systems requires parameterisations that characterise not only the broad behaviour but also its variation (e.g. between herds and regions). Data from outbreaks can be useful in developing suitable parameterisations. Using R0 as an example, values were estimated using a number of standard methods and compared to values calculated from the underlying epidemiological characteristics of simulated outbreaks. Both epidemiological characteristics and the method used to estimate R0 affect whether R0 is over- or under-estimated. These results do not suggest a universally preferred method for estimating R0 but highlight that an understanding of the underlying epidemiology of a system is required prior to method selection. Inaccurate estimation of R0 can have consequences for vaccine control - where R0 estimates are lower than the true value the population will be under-vaccinated. This is costly and result in ineffective control that allows some infection to remain. The infectious period and post outbreak immune period (POIP) of herds in endemic settings is unknown. These are likely different from disease-free settings where control measures are expected; for example, in FMD-free settings there is no herd-level POIP as infected herds are removed from the population. Mixture distributions were fitted to outputs from simulated outbreaks to give herd-level estimates for the infectious period and POIP. It is shown that, in the absence of intervention, there is a period of herd immunity following 65% of simulated outbreaks. Furthermore, analysis suggests a mean herd-level infectious period of 21.5 days – longer than previously used in the modelling of FMD transmission between herds. This work highlights the importance of obtaining and using herd-level estimates which are appropriate for endemic settings. Poor herd-level estimates of epidemiological characteristics can result in inadequate appreciation of transmission dynamics and key factors in the persistence of infection at regional scales. In turn this will compromise the design and implementation of control measures. As persistence was not observed at the herd level, a metapopulation model framework to explore endemic persistence in pastoral systems was developed. A population of 13000 herds (representative of Cameroon’s Adamawa region) was modelled allowing for local and transhumant contact. Although it was not possible to identify FMD specific parameters characterising between-herd disease spread, persistence and dynamics were explored for a limited range of contact and transmission parameters. The results indicate that seasonal transhumance can contribute to the persistence of infection at a regional level. The observed dynamics of infection and immunity are seasonal with immunity during the period of endemic stability greater than 60%. Timing of peak infection is dependent on seasonal variation in both contact between herds and vaccination. Short-term vaccine-derived immunity was modelled and is characteristic of the protection offered by FMD vaccines. The modelled seasonality of vaccination, and subsequent loss of vaccine-derived immunity, results in an increase in susceptible herds following the transhumant period. It is likely that this seasonal increase in susceptibility helps the persistence of infection as has been observed with other diseases such as measles. There is still much that needs to be understood about the dynamics of FMD transmission in endemic regions. Modelling can work well alongside targeted data collection to understand persistence, infection dynamics and assess control measures (particularly over long time scales) that are difficult to undertake in the field. Exploration of models, like that presented in this work, can highlight areas where data from the field would be beneficial to improve model parameterisation and better reflect the system of interest. Although long-term longitudinal tracking of infection at herd level over a range of scales is likely to be costly to collect and challenging to analyse, data of this nature would help inform both within-herd and between-herd models of transmission.