Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail...

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Published in:Mathematics (Basel) 2021-08, Vol.9 (16), p.1858
Main Authors: Nur, Wahyudin, Trisilowati, Suryanto, Agus, Kusumawinahyu, Wuryansari Muharini
Format: Article
Language:English
Subjects:
basic reproduction number
Biological control
biological control agent
Eigenvalues
Equilibrium
Food science
Health education
Intervention
Liapunov functions
Mathematical models
Mollusks
Number systems
Ordinary differential equations
Parasites
Parasitic diseases
Population
Population control
Predators
Routh-Hurwitz criterion
schistosomiasis model
snail predator
Stability analysis
Tropical diseases
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Summary:Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail predator as a biological control agent. We prove that the solutions of the model are non-negative and bounded. The existence condition of equilibrium points is investigated. We determine the basic reproduction number when the predator goes to extinction and when the predator survives. The local stability condition of disease-free equilibrium point is proved using linearization, and the Lienard–Chipart and Routh–Hurwitz criteria. We use center-manifold theory to prove the local stability condition of the endemic equilibrium points. Furthermore, we constructed a Lyapunov function to investigate the global stability condition of the disease-free equilibrium points. To support the analytical results, we presented some numerical simulation results. Our findings suggest that a snail predator as a biological control agent can reduce schistosomiasis prevalence. Moreover, the snail-predator birth rate plays an essential role in controlling schistosomiasis spread.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9161858