Stochastic Model of Bovine Babesiosis with Juvenile and Adult Cattle

A stochastic model for Bovine Babesiosis (BB) including ticks, and both juvenile and adult cattle is developed. This model is formulated by a system of continuous-time Markov chains (CTMCs) that is derived based on an extension of the deterministic ordinary differential equation model developed by S...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2020-05, Vol.82 (6), p.64-64, Article 64
Main Authors: Wang, Xueying, Saad-Roy, Chadi M., van den Driessche, P.
Format: Article
Language:English
Subjects:
Babesiosis
Branching (mathematics)
Cattle
Cell Biology
Conditional probability
Continuous time systems
Differential equations
Extinction
Infectivity
Life Sciences
Markov chains
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Ordinary differential equations
Original Article
Outbreaks
Parameters
Probability theory
Statistical analysis
Stochastic models
Stochasticity
Ticks
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Summary:A stochastic model for Bovine Babesiosis (BB) including ticks, and both juvenile and adult cattle is developed. This model is formulated by a system of continuous-time Markov chains (CTMCs) that is derived based on an extension of the deterministic ordinary differential equation model developed by Saad-Roy et al. (Bull Math Biol 77:514–547, 2015). The nonlinear CTMC model is approximated by a multitype branching process, giving a theoretical estimate of the probability of an outbreak of BB. Unlike the deterministic dynamics where the basic reproduction number is a sharp threshold parameter, the stochastic model indicates that there is always a positive probability of disease extinction within the cattle population. For parameter values from Colombia data, conditional probability distributions are numerically obtained for the time to disease extinction or outbreak, and are found to depend on the host type at the initiation of infection. The models with and without the inclusion of juvenile cattle are compared, and our result highlights that neglecting juvenile bovine in the models may lead to faulty predictions of critical disease statistics: particularly, it may underestimate the risk of infection. Endemic disease prevalence in adult cattle is examined for certain parameter values in the corresponding deterministic model. Notably, with long-lasting immunity, increased tick to juvenile infectivity decreases the proportion of infectious adults.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-020-00734-x