A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding

• Published in: Acta biotheoretica 2021-12, Vol.69 (4), p.511-541
• Main Authors: Kadaleka, Solomon, Abelman, Shirley, Tchuenche, Jean M.
• Format: Article
• Language: English
• Subjects: Cercaria; Disease transmission; Education; Evolutionary Biology; Gastropoda; Mathematical models; Molluscicides; Philosophy; Philosophy of Biology; Regular Article; Schistosomiasis; Sensitivity analysis
• ISSN: 0001-5342; 1572-8358
• DOI: 10.1007/s10441-021-09416-0

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number R 0 < 1 , while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, ε s (snails shedding rate of cercariae), p s (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and μ c (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome.