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

Mathematics Department, Purdue University, West Lafayette, IN 47907, USA.
Mathematical Biosciences (Impact Factor: 1.3). 02/2007; 205(1):83-107. DOI: 10.1016/j.mbs.2006.06.006
Source: PubMed


We study a system of partial differential equations which models the disease transmission dynamics of schistosomiasis. The model incorporates both the definitive human hosts and the intermediate snail hosts. The human hosts have an age-dependent infection rate and the snail hosts have an infection-age-dependent cercaria releasing rate. The parasite reproduction number R is computed and is shown to determine the disease dynamics. Stability results are obtained via both analytic and numerical studies. Results of the model are used to discuss age-targeted drug treatment strategies for humans. Sensitivity and uncertainty analysis is conducted to determine the role of various parameters on the variation of R. The effects of various drug treatment programs on disease control are compared in terms of both R and the mean parasite load within the human hosts.

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    • "Mathematical models are powerful tools for gaining insights into the transmission and control of infectious diseases, and can be used to address such an important issue. There have been a lot of mathematical models to investigate transmission dynamics of schistosomiasis ([5] [6] [15] [21] [23] and references therein). "
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    ABSTRACT: In this paper we formulate a dynamical model to study the transmission dynamics of schistosomiasis in humans and snails. We also incorporate bovines in the model to study their impact on transmission and controlling the spread of Schistosoma japonicum in humans in China. The dynamics of the model is rigorously analyzed by using the theory of dynamical systems. The theoretical results show that the disease free equilibrium is globally asymptotically stable if R0 < 1, and if R0 > 1 the system has only one positive equilibrium. The local stability of the unique positive equilibrium is investigated and sufficient conditions are also provided for the global stability of the positive equilibrium. The optimal control theory are further applied to the model to study the corresponding optimal control problem. Both analytical and numerical results suggest that: (a) the infected bovines play an important role in the spread of schistosomiasis among humans, and killing the infected bovines will be useful to prevent transmission of schistosomiasis among humans; (b) optimal control strategy performs better than the constant controls in reducing the prevalence of the infected human and the cost for implementing optimal control is much less than that for constant controls; and (c) improving the treatment rate of infected humans, the killing rate of the infected bovines and the fishing rate of snails in the early stage of spread of schistosomiasis are very helpful to contain the prevalence of infected human case as well as minimize the total cost.
    Preview · Article · Oct 2015 · Mathematical Biosciences and Engineering
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    • "We refer to Cushing [17] [18], Prüss [45], Swart [50], Kostova and Li [38], Bertoni [8], Magal and Ruan [44]. It is believed that such periodic solutions in age structured models are induced by Hopf bifurcations (Castillo-Chavez et al. [13], Inaba [33] [34], Zhang et al. [57]). Hopf bifurcation analysis has been considered for various classes of partial differential equations in Amann [2], Crandall and Rabinowitz [16], Da Prato and Lunardi [19], Guidotti and Merino [27], Koch and Antman [37], Sandstede and Scheel [48], and Simonett [49]. "
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    ABSTRACT: This article is devoted to investigate some dynamical properties of a structured population dynamic model with random walk on (0,+∞). This model has a nonlinear and nonlocal boundary condition. We reformulate the problem as an abstract non-densely defined Cauchy problem, and use integrated semigroup theory to study such a partial differential equation. Moreover, a Hopf bifurcation theorem is given for this model.
    Full-text · Article · Aug 2011 · Journal of Nonlinear Science
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    • "There are plenty of single disease dynamic models. A significant number focus on HIV/AIDS [22] [23] [24] [25] [26] or on the transmission dynamics of schistosomiasis [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]. Schistosomiasis model (24) considered in this study differs from those found in the literature in that we consider Schistosoma mansoni a human blood fluke which causes schistosomiasis and is the most widespread and the fresh water snail Biomphalaria glabrata serves as the main intermediate host, while the HIV/AIDS model (7) is an extension of the model by Murray [38] by including HIV therapy while neglecting the issue of seropositivity considered in [38]. "
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    ABSTRACT: We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.
    Full-text · Article · Feb 2011 · Computational and Mathematical Methods in Medicine
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