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Title: The temporal patterns of disease severity and prevalence in schistosomiasis

Abstract

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.

Authors:
; ;  [1];  [1];  [2];  [3];  [4]
  1. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano (Italy)
  2. (Switzerland)
  3. Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne (Switzerland)
  4. (Italy)
Publication Date:
OSTI Identifier:
22402543
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; DIFFERENTIAL EQUATIONS; DISEASES; DYNAMICS; FLUCTUATIONS; LIFE CYCLE; NONLINEAR PROBLEMS; OSCILLATIONS; PERIODICITY; PUBLIC HEALTH; SCHISTOSOMIASIS; SEASONAL VARIATIONS; TIME DEPENDENCE

Citation Formats

Ciddio, Manuela, Gatto, Marino, E-mail: marino.gatto@polimi.it, Casagrandi, Renato, E-mail: renato.casagrandi@polimi.it, Mari, Lorenzo, Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne, Rinaldo, Andrea, and Dipartimento di Ingegneria Civile, Edile ed Ambientale, Università di Padova, Via Loredan 20, 35131 Padova. The temporal patterns of disease severity and prevalence in schistosomiasis. United States: N. p., 2015. Web. doi:10.1063/1.4908202.
Ciddio, Manuela, Gatto, Marino, E-mail: marino.gatto@polimi.it, Casagrandi, Renato, E-mail: renato.casagrandi@polimi.it, Mari, Lorenzo, Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne, Rinaldo, Andrea, & Dipartimento di Ingegneria Civile, Edile ed Ambientale, Università di Padova, Via Loredan 20, 35131 Padova. The temporal patterns of disease severity and prevalence in schistosomiasis. United States. doi:10.1063/1.4908202.
Ciddio, Manuela, Gatto, Marino, E-mail: marino.gatto@polimi.it, Casagrandi, Renato, E-mail: renato.casagrandi@polimi.it, Mari, Lorenzo, Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne, Rinaldo, Andrea, and Dipartimento di Ingegneria Civile, Edile ed Ambientale, Università di Padova, Via Loredan 20, 35131 Padova. Sun . "The temporal patterns of disease severity and prevalence in schistosomiasis". United States. doi:10.1063/1.4908202.
@article{osti_22402543,
title = {The temporal patterns of disease severity and prevalence in schistosomiasis},
author = {Ciddio, Manuela and Gatto, Marino, E-mail: marino.gatto@polimi.it and Casagrandi, Renato, E-mail: renato.casagrandi@polimi.it and Mari, Lorenzo and Laboratory of Ecohydrology, ECHO/IIE/ENAC, École Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne and Rinaldo, Andrea and Dipartimento di Ingegneria Civile, Edile ed Ambientale, Università di Padova, Via Loredan 20, 35131 Padova},
abstractNote = {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.},
doi = {10.1063/1.4908202},
journal = {Chaos (Woodbury, N. Y.)},
number = 3,
volume = 25,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}