The modelling of African animal trypanosomiasis in KwaZulu-Natal, South Africa.
African animal trypanosomiasis (AAT), restricted to parts of the KwaZulu-Natal Province, is a disease which contributes signi cantly to the disease burden of cattle. Drug resistance is a constraint and dipping of cattle using insecticides has proved to be unsustainable. Even though the incidence of AAT has increased, little is known about the epidemiology of the disease in the region. To better understand the dynamics of AAT, mathematical modelling was done to investigate the interactions between the cattle, tsetse ies and bu aloes which are considered to be the reservoir host. In addition, a statistical analysis of the data collected from three sites around the Hluhluwe-iMfolozi Game Park was done to assess the interactions between the variables. A susceptible-infected (SI) model was constructed for the di erent classes of the population i.e. susceptible and infected cattle and tsetse ies and infected bu aloes. The basic reproduction number R0, a threshold determining whether the disease will die out or persist in the population, was derived using the next-generation matrix since we had two-hosts and one vector. R0 was used to assess which elements contribute to R0 (i.e. transmission of AAT from the bu aloes and cattle to the tsetse ies or tsetse ies to the cattle and buffaloes). The important element was found to be the transmission of AAT from bu aloes to ies. Sensitivity analysis was done using the partial rank correlation coe cients (PRCC) measure. PRCC values can show which parameters to target when looking at intervention measures and determine how to e ciently reduce AAT. The mortality rate of tsetse ies and their biting rate were determined to be the most important parameters. Generalized linear models (GLMs) were used to analyse the data since we had binary and count data. The AAT prevalence data was modelled using a binomial GLM, using the packed cell volume (PCV), which is an indicator of whether a cow has AAT or not, region i.e. whether the cow is located near or further away from the game park and month as the explanatory variables. PCV and region were found to be signi cant, so where the cattle are located seems to be important. The tsetse abundance data was modelled using Poisson GLMs, however the problem of overdispersion was evident and so alternative models were considered. Since there were excess zeroes for G. austeni, zero-in ated models were used and the best t was found to be the zero-in ated negative binomial, whereas the negative binomial model was used for G. brevipalpis to account for the overdispersion. Months 7 and 8 and year were found to be statistically signi cant for G.austeni. This could be because month 7 has the lowest minimum and maximum temperatures during the year and at lower temperatures, tsetse ies become less active and the pupal stage lengthens to around 50 days and the reproductive rate decreases. For G.brevipalpis only year was found to be statistically signi cant. The AAT prevalence data was t to the mathematical model using least squares, and the input parameters were estimated and used to calculate R0 again so that it is more site-speci c. Climate change was also brie y addressed, since it is predicted to a ect the geographical distribution of tsetse ies. Higher temperatures could have a big impact on the AAT situation because tsetse ies might modify their behaviour and shift their geographical range to regions that are cooler, which might put cattle populations in other regions at risk of AAT outbreaks.