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Journal of Biological Dynamics Volume 7, 2013 - Issue 1
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Original Articles

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Suzanne L. RobertsonDepartment of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond23284, VA, USA;Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus43210, OH, USACorrespondence[email protected]
,
Marisa C. EisenbergDepartments of Epidemiology and Mathematics, University of Michigan, Ann Arbor, MI, USA;Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus43210, OH, USA
&
Joseph H. TienDepartment of Mathematics, The Ohio State University, Columbus, OH, USA
Pages 254-275 | Received 05 Apr 2013, Accepted 02 Oct 2013, Published online: 01 Nov 2013

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O.C. Collins, T.S. Simelane & K.J. Duffy. (2019) Analyses of mathematical models for city population dynamics under heterogeneity. African Journal of Science, Technology, Innovation and Development 11:3, pages 323-337.
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Obiora Cornelius Collins & Kevin Jan Duffy. (2018) Optimal control of foliar disease dynamics for multiple maize varieties. Acta Agriculturae Scandinavica, Section B — Soil & Plant Science 68:5, pages 412-423.
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Xueying Wang & Jin Wang. (2015) Analysis of cholera epidemics with bacterial growth and spatial movement. Journal of Biological Dynamics 9:sup1, pages 233-261.
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Zhisheng Shuai & P. van den Driessche. (2015) Modelling and control of cholera on networks with a common water source. Journal of Biological Dynamics 9:sup1, pages 90-103.
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Articles from other publishers (39)

Yue Liu & Jize Wei. (2023) Stationary distribution and probability density function of a stochastic waterborne pathogen model with logistic growth. International Journal of Biomathematics 16:08.
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Xinxin Cheng, Yi Wang & Gang Huang. (2023) Edge-based compartmental modeling for the spread of cholera on random networks: A case study in Somalia. Mathematical Biosciences 366, pages 109092.
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Stephen Ekwueme Aniaku, Obiora Cornelius Collins & Ifeanyi Sunday Onah. (2023) Analysis and Optimal Control Measures of a Typhoid Fever Mathematical Model for Two Socio-Economic Populations. Mathematics 11:23, pages 4722.
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Tianli Jiang & Jinliang Wang. (2023) Modeling and analysis of a diffusive cholera model with seasonally forced intrinsic incubation period and bacterial hyperinfectivity. Journal of Mathematical Analysis and Applications 527:1, pages 127414.
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Jinling Zhou, Yu Yang & Cheng-Hsiung Hsu. (2023) Traveling waves of a discrete diffusive waterborne pathogen model with general incidence. Communications in Nonlinear Science and Numerical Simulation 126, pages 107431.
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Omprakash Singh Sisodiya, O. P. Misra & Joydip Dhar. (2023) Analysis of a temperature-dependent model for water-borne disease transmission dynamics. International Journal of Dynamics and Control 11:5, pages 2112-2126.
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Philip E. Paré, Axel Janson, Sebin Gracy, Ji Liu, Henrik Sandberg & Karl H. Johansson. (2023) Multilayer SIS Model With an Infrastructure Network. IEEE Transactions on Control of Network Systems 10:1, pages 295-307.
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Jin Wang. (2022) Mathematical Models for Cholera Dynamics—A Review. Microorganisms 10:12, pages 2358.
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Rujira Chaysiri, Garrick E. Louis & Wirawan Chinviriyasit. (2021) Modeling the health impact of water and sanitation service deficits on waterborne disease transmission. Advances in Difference Equations 2021:1.
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Isotein Adalia Ikiroma & Kevin George Pollock. (2020) Influence of weather and climate on cryptosporidiosis—A review. Zoonoses and Public Health 68:4, pages 285-298.
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O C Collins & J E Okeke. (2021) Analysis and multiple control measures for a typhoid fever disease model. Journal of Physics: Conference Series 1734:1, pages 012053.
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Lina Taing & Nga Dang. 2021. Handbook of Global Health. Handbook of Global Health 2211 2226 .
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Obiora Cornelius CollinsKevin Jan Duffy. (2020) Mathematical Analyses on the Effects of Control Measures for a Waterborne Disease Model with Socioeconomic Conditions. Journal of Computational Biology.
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Ifeanyi Sunday Onah, Obiora Cornelius Collins, Praise-God Uchechukwu Madueme & Godwin Christopher Ezike Mbah. (2020) Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model. International Journal of Mathematics and Mathematical Sciences 2020, pages 1-18.
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Xueying Wang & Feng-Bin Wang. (2019) Impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment. Journal of Mathematical Analysis and Applications, pages 123407.
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Philip E. Pare, Ji Liu, Carolyn L. Beck & Tamer Basar. (2019) Networked Infectious Disease–Contaminated Water Model. Networked Infectious Disease–Contaminated Water Model.
ABHISHEK SENAPATI, TRIDIP SARDAR & JOYDEV CHATTOPADHYAY. (2019) A CHOLERA METAPOPULATION MODEL INTERLINKING MIGRATION WITH INTERVENTION STRATEGIES — A CASE STUDY OF ZIMBABWE (2008–2009). Journal of Biological Systems 27:02, pages 185-223.
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Haifeng Song & Yuxiang Zhang. (2019) Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways. Electronic Journal of Qualitative Theory of Differential Equations:86, pages 1-19.
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Obiora Cornelius Collins & Kevin Jan Duffy. (2018) Analysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Study. Journal of Applied Mathematics 2018, pages 1-14.
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Jinling Zhou, Yu Yang & Tonghua Zhang. (2018) Global dynamics of a reaction–diffusion waterborne pathogen model with general incidence rate. Journal of Mathematical Analysis and Applications 466:1, pages 835-859.
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Anthony A. E. Losio & Steady Mushayabasa. (2018) Modeling the Effects of Spatial Heterogeneity and Seasonality on Guinea Worm Disease Transmission. Journal of Applied Mathematics 2018, pages 1-12.
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Omprakash Singh Sisodiya, O.P. Misra & Joydip Dhar. (2018) Dynamics of cholera epidemics with impulsive vaccination and disinfection. Mathematical Biosciences 298, pages 46-57.
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Omprakash Singh Sisodiya, O. P. Misra & Joydip Dhar. (2018) Pathogen Induced Infection and Its Control by Vaccination: A Mathematical Model for Cholera Disease. International Journal of Applied and Computational Mathematics 4:2.
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Jackeline Abad Torres & Sandip Roy. (2018) Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem. Automatica 89, pages 160-168.
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Sandeep Sharma & Nitu Kumari. (2017) Why to consider environmental pollution in cholera modeling?. Mathematical Methods in the Applied Sciences 40:18, pages 6348-6370.
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Giovanni Lo Iacono, Ben Armstrong, Lora E. Fleming, Richard Elson, Sari Kovats, Sotiris Vardoulakis & Gordon L. Nichols. (2017) Challenges in developing methods for quantifying the effects of weather and climate on water-associated diseases: A systematic review. PLOS Neglected Tropical Diseases 11:6, pages e0005659.
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Andrew F. Brouwer, Mark H. Weir, Marisa C. Eisenberg, Rafael Meza & Joseph N. S. Eisenberg. (2017) Dose-response relationships for environmentally mediated infectious disease transmission models. PLOS Computational Biology 13:4, pages e1005481.
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O. C. COLLINS & K. J. DUFFY. (2016) OPTIMAL CONTROL INTERVENTION STRATEGIES USING AN N-PATCH WATERBORNE DISEASE MODEL. Natural Resource Modeling 29:4, pages 499-519.
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Xueying Wang, Drew Posny & Jin Wang. (2016) A reaction-convection-diffusion model for cholera spatial dynamics. Discrete and Continuous Dynamical Systems - Series B 21:8, pages 2785-2809.
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O. C. COLLINS & K. S. GOVINDER. (2016) STABILITY ANALYSIS AND OPTIMAL VACCINATION OF A WATERBORNE DISEASE MODEL WITH MULTIPLE WATER SOURCES. Natural Resource Modeling 29:3, pages 426-447.
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Suzanne L. Robertson & Kevin A. Caillouët. (2016) A host stage-structured model of enzootic West Nile virus transmission to explore the effect of avian stage-dependent exposure to vectors. Journal of Theoretical Biology 399, pages 33-42.
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NITU KUMARI & SANDEEP SHARMA. (2016) DOES WATER DISINFECTANT PLAY A SUPPORTIVE ROLE IN THE SPREAD OF INFECTIOUS DISEASE? A MATHEMATICAL STUDY. Natural Resource Modeling 29:2, pages 259-288.
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Jackeline Abad Torres & Sandip Roy. (2015) Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem. Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem.
Andrew F. Brouwer, Rafael Meza & Marisa C. Eisenberg. (2015) Transmission heterogeneity and autoinoculation in a multisite infection model of HPV. Mathematical Biosciences 270, pages 115-125.
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O.C. Collins, Suzanne L. Robertson & K.S. Govinder. (2015) Analysis of a waterborne disease model with socioeconomic classes. Mathematical Biosciences 269, pages 86-93.
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URMI GHOSH-DASTIDAR & SUZANNE LENHART. (2015) MODELING THE EFFECT OF VACCINES ON CHOLERA TRANSMISSION. Journal of Biological Systems 23:02, pages 323-338.
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Charles N. Haas. (2015) Microbial Dose Response Modeling: Past, Present, and Future. Environmental Science & Technology 49:3, pages 1245-1259.
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O.C. Collins & K.S. Govinder. (2014) Incorporating heterogeneity into the transmission dynamics of a waterborne disease model. Journal of Theoretical Biology 356, pages 133-143.
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