Schistosomiasis model with treatment, habitat modification and biological control

Wahyudin Nur; Trisilowati; Agus Suryanto; Wuryansari Muharini Kusumawinahyu; Wahyudin Nur; Trisilowati; Agus Suryanto; Wuryansari Muharini Kusumawinahyu

doi:10.3934/mbe.2022643

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13799-13828. doi: 10.3934/mbe.2022643

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Research article

Schistosomiasis model with treatment, habitat modification and biological control

1.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia
2.
Department of Mathematics, Universitas Sulawesi Barat, Majene 91411, Indonesia

Academic Editor: Jia Li

Received: 17 April 2022 Revised: 07 August 2022 Accepted: 17 August 2022 Published: 19 September 2022

Schistosomiasis is a parasitic disease caused by Schistosoma worm infection. Some species of snails can serve as the intermediate hosts for the parasite. Numerous interventions have been performed to repress the snail population. One of them is the use of molluscicide. Nevertheless, it is debated that molluscicide intervention has negative impacts on the ecosystem. To investigate the impact of more environmentally friendly interventions, we develop a schistosomiasis model with treatment, habitat modification and biological control. The biological control agent examined in our model is a snail predator. Moreover, to investigate the impact of snail habitat modification, we assume that the snail population grows logistically. We show that all solutions of our model are non-negative and bounded. We also study the existence and stability conditions of equilibrium points. The basic reproduction numbers are determined using the next-generation operator. Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. To examine the global behavior of our model, we use asymptotically autonomous system theory and construct a Lyapunov function. We perform several numerical simulations to validate and support our deductive results. Our results show that early treatment can reduce the basic reproduction number and schistosomiasis cases. In addition, modifying snail habitat and releasing the snail predator at the snail habitat can reduce schistosomiasis prevalence. We suggest using snail predators which can hunt and kill snails effectively as a biological control agent.
- schistosomiasis model,
- treatment,
- snail predator,
- logistic growth,
- biological control agent,
- snail habitat modification,
- asymptotically autonomous systems
Citation: Wahyudin Nur, Trisilowati, Agus Suryanto, Wuryansari Muharini Kusumawinahyu. Schistosomiasis model with treatment, habitat modification and biological control[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13799-13828. doi: 10.3934/mbe.2022643

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Abstract

Schistosomiasis is a parasitic disease caused by Schistosoma worm infection. Some species of snails can serve as the intermediate hosts for the parasite. Numerous interventions have been performed to repress the snail population. One of them is the use of molluscicide. Nevertheless, it is debated that molluscicide intervention has negative impacts on the ecosystem. To investigate the impact of more environmentally friendly interventions, we develop a schistosomiasis model with treatment, habitat modification and biological control. The biological control agent examined in our model is a snail predator. Moreover, to investigate the impact of snail habitat modification, we assume that the snail population grows logistically. We show that all solutions of our model are non-negative and bounded. We also study the existence and stability conditions of equilibrium points. The basic reproduction numbers are determined using the next-generation operator. Linearization combined with the Routh-Hurwitz criterion is used to prove the local stability condition of disease-free equilibrium points. Bifurcation theory is applied to investigate the local stability condition of the endemic equilibrium points. To examine the global behavior of our model, we use asymptotically autonomous system theory and construct a Lyapunov function. We perform several numerical simulations to validate and support our deductive results. Our results show that early treatment can reduce the basic reproduction number and schistosomiasis cases. In addition, modifying snail habitat and releasing the snail predator at the snail habitat can reduce schistosomiasis prevalence. We suggest using snail predators which can hunt and kill snails effectively as a biological control agent.

References

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