Ciddio Manuela, Mari Lorenzo, Gatto Marino, Rinaldo Andrea, Casagrandi Renato
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy.
Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne, Switzerland.
Chaos. 2015 Mar;25(3):036405. doi: 10.1063/1.4908202.
Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.
血吸虫病是世界上最广泛传播的公共卫生问题之一。在这项工作中，我们引入了一个关于其传播和动态的生态流行病学模型，目的是解释疾病严重程度和流行率的年内和年际波动。该模型采用非线性微分方程组的形式，纳入了与血吸虫生命周期相关的生物学复杂性，包括蜗牛体内的潜伏期（即从初始感染到具有传染性之间的时间）。非线性分析用于探索产生不同时间模式（稳态、地方病、周期性和混沌）的参数条件。对于时间不变模型，我们在人类和蜗牛感染参数空间中识别出一个跨临界分岔和一个霍普夫分岔。第一个对应地方病平衡点的出现，而后者标志着向年际周期性振荡的转变。然后，我们研究了一个更现实的时变模型，其中假设中间宿主种群的繁殖力随季节变化。我们表明，对于繁殖力季节性变化幅度较大但现实的值，季节性可以导致一系列倍周期分岔，从而导致混沌。
