Article

# 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: 1.45). 02/2007; 205(1):83-107. DOI: 10.1016/j.mbs.2006.06.006 Source: PubMed

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**ABSTRACT:**We developed a stochastic model for quantitative risk assessment for the Schistosoma mansoni (SM) parasite, which causes an endemic disease of public concern. The model provides answers in a useful format for public health decisions, uses data and expert opinion, and can be applied to any landscape where the snail Biomphalaria glabrata is the main intermediate host (South and Central America, the Caribbean, and Africa). It incorporates several realistic and case-specific features: stage-structured parasite populations, periodic praziquantel (PZQ) drug treatment for humans, density dependence, extreme events (prolonged rainfall), site-specific sanitation quality, environmental stochasticity, monthly rainfall variation, uncertainty in parameters, and spatial dynamics. We parameterize the model through a real-world application in the district of Porto de Galinhas (PG), one of the main touristic destinations in Brazil, where previous studies identified four parasite populations within the metapopulation. The results provide a good approximation of the dynamics of the system and are in agreement with our field observations, i.e., the lack of basic infrastructure (sanitation level and health programs) makes PG a suitable habitat for the persistence and growth of a parasite metapopulation. We quantify the risk of SM metapopulation explosion and quasi-extinction and the time to metapopulation explosion and quasi-extinction. We evaluate the sensitivity of the results under varying scenarios of future periodic PZQ treatment (based on the Brazilian Ministry of Health's plan) and sanitation quality. We conclude that the plan might be useful to slow SM metapopulation growth but not to control it. Additional investments in better sanitation are necessary.Risk Analysis 11/2013; · 2.28 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**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.Journal of Mathematical Biology 07/2011; 65(2):201-36. · 2.37 Impact Factor -
##### Article: The Dynamics of Growing Islets and Transmission of Schistosomiasis Japonica in the Yangtze River.

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**ABSTRACT:**We formulate and analyze a system of ordinary differential equations for the transmission of schistosomiasis japonica on the islets in the Yangtze River, China. The impact of growing islets on the spread of schistosomiasis is investigated by the bifurcation analysis. Using the projection technique developed by Hassard, Kazarinoff and Wan, the normal form of the cusp bifurcation of codimension 2 is derived to overcome the technical difficulties in studying the existence, stability, and bifurcation of the multiple endemic equilibria in high-dimensional phase space. We show that the model can also undergo transcritical bifurcations, saddle-node bifurcations, a pitchfork bifurcation, and Hopf bifurcations. The bifurcation diagrams and epidemiological interpretations are given. We conclude that when the islet reaches a critical size, the transmission cycle of the schistosomiasis japonica between wild rats Rattus norvegicus and snails Oncomelania hupensis could be established, which serves as a possible source of schistosomiasis transmission along the Yangtze River.Bulletin of Mathematical Biology 04/2014; · 2.02 Impact Factor

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