A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies

Zhang, Pei; Feng, Zhilan; Milner, Fabio

doi:10.1016/j.mbs.2006.06.006

Cited by 31 publications

(18 citation statements)

References 25 publications

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“…Current evidence supports the view that selection for resistance to PZQ may be occurring in schistosome populations and natural schistosome strains exhibit varying resistance to treatment with PZQ (Cioli 2000;Fallon et al 1997;Ismail et al 1999). Due to the age-dependence in schistosome infections in humans, various age-targeted treatment strategies have been adopted in different populations, and mathematical models have been used to assess the cost-effectiveness of the disease control programs (Chan et al 1995;Zhang et al 2007a).…”

Section: Introductionmentioning

confidence: 78%

“…(4) In this section, we study the dynamical behaviors of the system (4) by analyzing the mathematical properties of the system, including the existence and stability of biologically feasible equilibrium points and possible bifurcations. Using a similar approach as in Zhang et al (2007a) we can show that solutions of the system (4) are defined for all t ≥ 0 and will remain nonnegative and bounded for all time.…”

Section: The Modelmentioning

confidence: 99%

“…Let n(t, a) denote the density function of human hosts of age a at time t, and let p(t, a) denote the density function of parasites carried by human hosts of age a at time t. Based on the models in Anderson and May (1978), Dobson (1988), Hadeler (1984, Hadeler and Dietz (1983), and Zhang et al (2007a), the equations for n(t, a) and p(t, a) take the forms (a derivation of these equations is given in the Appendix):…”

Section: The Modelmentioning

confidence: 99%

“…Each type of the snail populations is divided into two sub-classes: uninfected (S k , k = 1, 2) and infected (I k , k = 1, 2). Following the model structure in Zhang et al (2007a) (the model there includes only a single type of snail host), the disease dynamics of the snail population is described by the following ordinary differential equations:…”

Section: The Modelmentioning

confidence: 99%

“…The constants β j and σ j depend on the ages of human hosts (see Zhang et al 2007a), and examples of these functions are demonstrated in Fig. 5.…”

Section: Competitive Outcomes Between Two Types Of Hostsmentioning

confidence: 99%

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Evolution of host resistance to parasite infection in the snail–schistosome–human system

Yang

Feng

et al. 2011

J. Math. Biol.

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The evolutionary strategies that emerge within populations can be dictated by numerous factors, including interactions with other species. In this paper, we explore the consequences of such a scenario using a host-parasite system of human concern. By analyzing the dynamical behaviors of a mathematical model we investigate the evolutionary outcomes resulting from interactions between Schistosoma mansoni and its snail and human hosts. The model includes two types of snail hosts representing resident and mutant types. Using this approach, we focus on establishing evolutionary stable strategies under conditions where snail hosts express different life-histories and when drug treatment is applied to an age-structured population of human hosts. Results from this work demonstrate that the evolutionary trajectories of host-parasite interactions can be varied, and at times, counter-intuitive, based on parasite virulence, host resistance, and drug treatment.

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Section: Introductionmentioning

confidence: 78%

Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

“…The constants β j and σ j depend on the ages of human hosts (see Zhang et al 2007a), and examples of these functions are demonstrated in Fig. 5.…”

Section: Competitive Outcomes Between Two Types Of Hostsmentioning

confidence: 99%

See 3 more Smart Citations

Evolution of host resistance to parasite infection in the snail–schistosome–human system

Yang

Feng

et al. 2011

J. Math. Biol.

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Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Wu,

Salmaniw,

Wang

2024

J. Math. Biol.

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Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number $${\mathcal {R}}_0$$ R 0 and show that the disease-free periodic solution is globally attractive when $${\mathcal {R}}_0<1$$ R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when $${\mathcal {R}}_0>1$$ R 0 > 1 . Moreover, we find that $${\mathcal {R}}_0$$ R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

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Hopf Bifurcation for a Maturity Structured Population Dynamic Model

2011

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A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies

Cited by 31 publications

References 25 publications

Evolution of host resistance to parasite infection in the snail–schistosome–human system

Evolution of host resistance to parasite infection in the snail–schistosome–human system

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Hopf Bifurcation for a Maturity Structured Population Dynamic Model

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