Modeling Host-Parasite Systems

Feng9974389研究人员和她的同事通过开发数学模型来研究和分析寄生吸虫与它们的无脊椎动物和脊椎动物宿主之间的复杂相互作用，这些模型允许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-微分方程组理论，提出了基于微分方程组的连续确定性模型，并进行了分析。为验证模型而收集的数据使用标准统计技术进行拟合。较简单的初始模型的验证是通过获取两个或更多时间点的人类宿主感染流行率值，并估计可获得数据的其他时间点的感染流行率来完成的。开展了一项合作研究，将寄生虫学家的理论和经验经验与数学家的建模和理论专业知识相结合，以研究宿主-寄生虫相互作用的模型。该项目的范围有三个方面：*第一，模拟宿主-寄生虫的相互作用，由于生物学考虑，模型越来越复杂；*第二，研究每个模型的数学特性及其对生物和生态的影响，如种群控制或潜在的物种灭绝；*第三，通过比较模型结果与现场数据来验证模型。这个项目通过为研究自然系统提供有用的模型，通过分析它们对影响其动力学的参数的敏感性，以及通过允许将系统的复杂性组织成等级，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需要治疗才能根除这种疾病的血吸虫病病例的比例，以及药物诱导的寄生虫变异和一种以上确定宿主的存在对这种疾病传播动态的影响。重要的是有可能将本项目中开发的模型扩展到涉及三个或更多个或更多的更复杂的系统，或随机环境变异性。

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.