Global analysis of a schistosomiasis infection model with biological control

Diaby, Mouhamadou; Iggidr, Abderrahman; Sy, Mamadou; Sène, Abdou

doi:10.1016/j.amc.2014.08.061

Cited by 18 publications

(14 citation statements)

References 13 publications

(28 reference statements)

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“…In reservoir host body, some cercariae survive and become adult shistosoma worm [3,6,7]. Several mathematical models are developed to study the spread of schistosomiasis in human, mammals, and snail population [8,9]. However, these two models do not take into account the density of the parasite in environment.…”

Section: Schistosomiasismentioning

confidence: 99%

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Nur¹,

Trisilowati²,

Suryanto³

et al. 2021

Advances in Social Science, Education and Humanities Research

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In this work, a deterministic mathematical model of schistosomiasis transmission dynamics is discussed. In rural areas, many people work as a cattle farmer. Cattle farmers in endemic areas are very susceptible to schistosoma worm infection. To study the dynamics of schistosomiasis spread in traditional cattle farmer communities, we develop a mathematical model by considering human, cattle, and snail population as well as parasite density in environment. The model is expressed as a system of first order differential equations. Firstly, we verify the non-negativity and boundedness of the solutions of the model. After determining the equilibrium points of the system, we determine the basic reproduction number. Linearization and Routh Hurwitz condition are used to analyze the local stability condition of the disease free equilibrium point. Center manifold theory is used to study the local stability condition of the endemic equilibrium point. We prove global stability condition of the disease free equilibrium point by formulating suitable Lyapunov function and using LaSalle invariance principle. Several numerical simulations are presented. Our results show that the farmer should keep the cattle, water, and food clean. In addition, the farmer should use molluscicide in their farm area and give schistosomiasis drug to the cattle, regularly.

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Section: Schistosomiasismentioning

confidence: 99%

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Nur¹,

Trisilowati²,

Suryanto³

et al. 2021

Advances in Social Science, Education and Humanities Research

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show abstract

“…After the pioneering work of Macdonald [5], the dynamics properties (including stability, persistence, and oscillatory behavior) of the schistosomiasis models that have significant biological background have been one of the most active areas of research and have attracted great attention of many researchers. Many excellent and interesting results have been obtained (see [6]- [18]). Besides, a simplification of the two-strain, vector-host model was proposed by Feng and Velasco-Hernández [19] for Dengue fever.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of a <i>Schistosomiasis japonicum</i> Model with Time Delay

Zhang¹,

Gao²,

Cao³

et al. 2019

JAMP

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In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equations, the local stability of the equilibria is investigated. And it proves that Hopf bifurcations occur when the time delay passes through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using techniques from the normal form theory and Center Manifold Theorem. Some numerical simulations which support our theoretical analysis are also conducted.

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“…Moreover, schistosomiasis cannot be eradicated if the only intervention is health education [13]. Diaby et al [15] proposed a schistosomiasis model with biological control, i.e., competitor-resistant snails. They found that competitor-resistant snails can be used to manage the spread of schistosomiasis.…”

Section: Introductionmentioning

confidence: 99%

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

et al. 2021

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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.

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Global analysis of a schistosomiasis infection model with biological control

Cited by 18 publications

References 13 publications

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Dynamical Analysis of a <i>Schistosomiasis japonicum</i> Model with Time Delay

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

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Global analysis of a schistosomiasis infection model with biological control

Cited by 18 publications

References 13 publications

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Dynamical Analysis of a &lt;i&gt;Schistosomiasis japonicum&lt;/i&gt; Model with Time Delay

Schistosomiasis Model Incorporating Snail Predator as Biological Control Agent

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Dynamical Analysis of a <i>Schistosomiasis japonicum</i> Model with Time Delay