Outbreak or extinction of bovine cysticercosis and human taeniasis: A Stochastic modelling approach

Abstract

Bovine cysticercosis and human taeniasis are neglected food-borne infections that pose challenges to food safety, peoples’ health and the economy of rural farmers who depend on livestock keeping. In this paper, the continuous time Markov chain (CTMC) stochastic model is formulated based on its corresponding deterministic model and rigorously analyzed to study the dynamics of cysticercosis in cattle and taeniasis in humans. The multitype branching process is adopted to compute the stochastic threshold and numerical simulations for the CTMC model with 10,000 sample paths are used to compute probabilities of diseases’ extinction when initial conditions for infected classes are varied. The results show that when there is disease outbreak, the solutions of CTMC stochastic model are relatively close to deterministic model solutions. The analytical and numerical results for probability of diseases’ extinction are in good agreement when initially there is no infectious human. Some variations in probability of diseases’ extinction are due to infectious beef being considered a discrete number in CTMC model. The results show further that the diseases' extinction probability is high when the diseases emerge from a small number of T. saginata eggs or from infected cattle. However, the probability becomes low when there is at least an infectious beef at the beginning of the diseases' outbreak.