A mathematical model to inform on desirable dog-rabies control methods in an urban setting: a case study of Arusha-Tanzania

Abstract

Rabies is a zoonotic, viral disease that causes an acute brain inflammation in mammals. It is transmitted through the saliva of infected animals via bites, scratches or contact with infectious tissue. In this study, we formulate a deterministic model which measures the effects of culling and vaccination on dog mediated transmission of rabies for urban areas near wildlife, using the Arusha region as an example. Various parameter values were deduced from five years worth of survey data on Arusha’s dog population and dog vaccination coverage from the Mbwa wa Africa group, a Non Governmental Organisation and from records of dog bite incidence and deaths cases from the Ministry of Livestock and Fisheries, Tanzania. Three distinct dog populations were assumed: domestic dogs, stray dogs and Pastoralist dogs. The basic reproduction number R 0 and effective reproduction number R for rabies were computed to estimate transmission and found to be 1.9 and 1.2 respectively. The disease free equilibrium " e was also computed. When R < 1 it implies that it is globally asymptotically stable in the feasible region . When R e e > 1, it implies that, there is an equilibrium point which is endemic and locally asymptotically stable. According to the sensitivity indices, infection rate of stray dogs is the most positive sensitive parameter and natural death rate of stray dogs is the most negative sensitive parameter. This study proposes putting much emphasis on the most positive and most negative sensitive parameters when fighting against dog-rabies transmission in urban areas near wildlife reservoirs. Under the assumption that a dog is immune to rabies for 3 years once vaccinated, the numerical simulations of the formulated model predict that the number of infected stray dogs will increase to its highest in 2020. However, the number of infected domestic dogs is expected to decline to its minimum in 2020, while the number of infected Pastoralist dogs will stay similar the same as the previous years in 2020. These results show that, rabies incidence for the infected stray dogs is the highest followed by the incidence for infected Pastoralist dogs and lastly for the infected domestic dogs. The numerical simulation of the reproduction number shows that dog mass vaccination is the most appropriate method in the long term to control rabies transmission among dog sub-populations for urban areas near wildlife reservoirs such as Arusha. Culling on the other hand, is effective at the moment in time when it is practiced, but its protective effect quickly decreases after just 6 to 8 months when all culled dogs will have been replaced by un-vaccinated new born puppies.