Modeling Host-Parasite Systems

研究人员和她的同事们通过建立数学模型来研究和分析寄生吸虫与其无脊椎动物和脊椎动物宿主之间复杂的相互作用，这些模型可以预测宿主和寄生虫的种群动态变化。利用动力系统理论和积分微分方程理论，提出并分析了基于微分方程组的连续确定性模型。为验证模型而收集的数据使用标准统计技术进行拟合。对较简单的初始模型的验证是通过在两个或多个时间点获取人类宿主感染的流行值，并在有数据的其他时间点估计感染的流行率来完成的。一项合作研究将结合寄生虫学家的理论和经验经验以及数学家的建模和理论专业知识来研究宿主-寄生虫相互作用的模型。这个项目的范围有三个方面：第一，模拟宿主-寄生虫的相互作用，由生物学因素驱动的模型越来越复杂；第二，研究每个模型的数学性质及其生物学和生态学意义，如人口控制或潜在的物种灭绝；*第三，通过模型结果与现场数据的对比，对模型进行验证。该项目通过提供可用的模型来研究自然系统，通过分析它们对影响其动力学的参数的敏感性，并通过允许将系统的复杂性构建为层次结构，显著地提高了我们对宿主-寄生虫系统动力学的认识和理解。一个具体的例子是确定为根除该病而需要治疗的血吸虫病病例的比例，以及药物诱导的寄生虫变异和不止一种确定宿主的存在对这种疾病传播动态的影响。同样重要的是，将本项目中开发的模型扩展到涉及三个或更多方面的更复杂系统，或随机环境可变性的可能性。

Feng9974389 The investigators and her colleagues study and analyze thecomplex interactions between parasitic trematodes and theirinvertebrate and vertebrate hosts by developing mathematicalmodels that allow the prediction of changes in the populationdynamics of both hosts and parasites. Continuous deterministicmodels based on systems of differential equations are proposedand analyzed using the theory of dynamical systems and integraland differential equations. Data gathered for the validation ofthe models is fitted using standard statistical techniques.Validation of the simpler initial models is done by taking theprevalence values of infection of human hosts at two or morepoints in time, and estimating prevalence of infection at otherpoints in time for which data is available. A collaborative study is undertaken that combines thetheoretical and empirical experience of a parasitologist and themodeling and theoretical expertise of mathematicians toinvestigate models of host-parasite interactions. The scope ofthis project is threefold: *First, to model host-parasite interactions, withincreasingly complex models motivated by biologicalconsiderations; *second, the study of mathematical properties of each modeland their biological and ecological implications such aspopulation control or potential species extinction; *third, the validation of the models through comparison ofmodel results with field data. This project significantlyadvances our knowledge and understanding of the dynamics ofhost-parasite systems, by providing usable models to studynatural systems, by analyzing their sensitivity to the parametersaffecting their dynamics, and by allowing the structuring of thecomplexities of the systems into hierarchies. A specific exampleis the determination of the proportion of cases ofschistosomiasis that need to be treated for the disease to beeradicated, as well as the effect of drug-induced parasitemutation and the existence of more than one species of definitivehosts on the dynamics of transmission of this ailment. Just asimportant is the possibility of extending the models developed inthis project to more complex systems involving three or morespecies, or stochastic environmental variability.