A cholera transmission model incorporating the impact of medical resources

Chayu Yang; Jin Wang; Chayu Yang; Jin Wang

doi:10.3934/mbe.2019261

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5226-5246. doi: 10.3934/mbe.2019261

Previous Article Next Article

Research article Special Issues

A cholera transmission model incorporating the impact of medical resources

Chayu Yang ,
Jin Wang ^,

Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Ave., Chattanooga, TN 37403, USA

Received: 25 November 2018 Accepted: 03 April 2019 Published: 06 June 2019

We propose a mathematical model for the transmission dynamics of cholera under the impact of available medical resources. The model describes the interaction between the human hosts and the pathogenic bacteria and incorporates both the environment-to-human and human-to-human transmission routes. We conduct a rigorous equilibrium analysis to the model and establish the global asymptotic stability of the disease-free equilibrium when $\mathcal{R}_0 \leq 1$ and that of the endemic equilibrium when $\mathcal{R}_0 > 1$. As a realistic case study, we apply our model to the Yemen cholera outbreak during 2017–2018. By fitting our simulation results to the epidemic data published by the World Health Organization, we find that different levels of disease prevalence and severity are linked to different geographical regions in this country and that cholera prevention and intervention efforts should be implemented strategically with respect to these regions in Yemen.
- epidemic modeling,
- cholera outbreak,
- medical resource,
- stability
Citation: Chayu Yang, Jin Wang. A cholera transmission model incorporating the impact of medical resources[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5226-5246. doi: 10.3934/mbe.2019261

Related Papers:

Abstract

We propose a mathematical model for the transmission dynamics of cholera under the impact of available medical resources. The model describes the interaction between the human hosts and the pathogenic bacteria and incorporates both the environment-to-human and human-to-human transmission routes. We conduct a rigorous equilibrium analysis to the model and establish the global asymptotic stability of the disease-free equilibrium when $\mathcal{R}_0 \leq 1$ and that of the endemic equilibrium when $\mathcal{R}_0 > 1$. As a realistic case study, we apply our model to the Yemen cholera outbreak during 2017–2018. By fitting our simulation results to the epidemic data published by the World Health Organization, we find that different levels of disease prevalence and severity are linked to different geographical regions in this country and that cholera prevention and intervention efforts should be implemented strategically with respect to these regions in Yemen.

References

[1]	D. M. Hartley, J. G. Morris and D. L. Smith, Hyperinfectivity: A critical element in the ability of V. cholerae to cause epidemics? PLoS Med., 3 (2006), 0063–0069.
[2]	E. J. Nelson, J. B. Harris, J. G. Morris, et al., Cholera transmission: The host, pathogen and bacteriophage dynamics, Nat. Rev. Microbiol., 7 (2009), 693–702.
[3]	D. He, X. Wang, D. Gao, et al., Modeling the 2016-2017 Yemen cholera outbreak with the impact of limited medical resources, J. Theor. Biol., 451 (2018), 80–85.
[4]	A. Camacho, M. Bouhenia, R. Alyusfi, et al., Cholera epidemic in Yemen, 2016-18: an analysis of surveillance data, Lancet Glob. Health, published on line May 3, 2018. Available from: http: //doi.org/10.1016/S2214-109X(18)30230-4.
[5]	Z. Mukandavire, S. Liao, J. Wang, et al., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, P. Natl. Acad. Sci. USA, 108 (2011), 8767–8772.
[6]	A. R. Tuite, J. H. Tien, M. C. Eisenberg, et al., Cholera epidemic in Haiti, 2010 – using a trans-mission model to explain spatial spread of disease and identify optimal control interventions, Ann. Intern. Med., 154 (2011), 593–601.
[7]	P. R. Mason, Zimbabwe experiences the worst epidemic of cholera in Africa, J. Infect. Dev. Countr., 3 (2009), 148–151.
[8]	WHO cholera fact sheet, 20031 February 2018. Available from: http://www.who.int/en/news-room/fact-sheets/detail/cholera.
[9]	WHO report on global surveillance of epidemic-prone infectious diseases, 2000: 39-54. Available from: http://www.who.int/csr/resources/publications/surveillance/WHO_Report_Infectious_Diseases.pdf.
[10]	G. Zorlu, Cholera vaccine deployed to control African outbreak, Nature, News and Comment, June 2012.
[11]	S. Shin, S. N. Desai, B. K. Sah, et al., Oral vaccines against cholera, Clin. Infect. Dis., 52 (2011), 1343–1349.
[12]	S. Batterman, J. Eisenberg, R. Hardin, et al., Sustainable control of water-related infectious dis-eases: A review and proposal for interdisciplinary health-based systems research, Environ. Health Persp., 117 (2009), 1023–1032.
[13]	E. D. Mintz and R. V. Tauxe, Cholera in Africa: a closer look and a time for action, J. Infect. Dis., 208 (2013), S4–7.
[14]	S. Cumberland, An old enemy returns, B. World Health Organ., 87 (2009), 85–86.
[15]	D. Posny and J. Wang, Modeling cholera in periodic environments, J. Biol. Dynam., 8 (2014), 1–19.
[16]	J. H. Tien and D. J. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, B. Math. Biol., 72 (2010), 1506–1533.
[17]	X. Wang, D. Posny and J. Wang, A reaction-convection-diffusion model for cholera spatial dy-namics, Discrete Cont. Dyn. B, 21 (2016), 2785–2809.
[18]	C. Yang, X. Wang, D. Gao, et al., Impact of awareness programs on cholera dynamics: Two modeling approaches, B. Math. Biol., 79 (2017), 2109–2131.
[19]	WHO survey on Yemen's health system. Available from: http://www.emro.who.int/media/news/survey-reveals-extent-of-damage-to-yemens-health-system.html.
[20]	WHO Weekly Epidemiology Bulletin, 21-27 May 2018.
[21]	WHO Yemen cholera situation reports. Available from: http://www.emro.who.int/yem/yemeninfocus/situation-reports.html.
[22]	R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
[23]	P. van den Driessche and J. Watmough, Reproduction number and subthreshold endemic equilibria for compartment models of disease transmission, Math. Biosci., 180 (2002), 29–48.
[24]	O. Diekmann, J. A. P. Heesterbeek and A. J. Metz, On the definition and the computation of the basic reproduction ratio R₀ in models for infectious diseases in heterogeneous population, J. Math. Biol., 28 (1990), 365–382.
[25]	J. P. LaSalle, The stability of dynamical systems, Regional Conference Series in Applied Mathe-matics, SIAM, Philadelphia, 1976.
[26]	H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407–435.
[27]	D. Gao and S. Ruan, An SIS patch model with variable transmission coefficients, Math. Biosci., 232 (2011), 110–115.
[28]	M. Y. Li and J. S. Muldowney, Dynamics of differential equations on invariant manifolds, J. Differ. Equations, 168 (2000), 295–320.
[29]	M. Y. Li, J. S. Muldowney and P. V. D. Driessche, Global stability of SEIRS models in epidemiol-ogy, Canadian Appl. Math. Quart., 7 (1999), 409–425.
[30]	Wikipedia page for Yemen. Available from: http://en.wikipedia.org/wiki/Yemen.
[31]	WHO Global health observatory data repository: Life expectancy, 2013. Available from: http: //apps.who.int/gho/data/view.main.680?lang=en.
[32]	ClimateandAverageWeatherinYemen.Availablefrom: http://weather-and-climate.com/average-monthly-Rainfall-Temperature-Sunshine-in-Yemen.
[33]	World Climate Guide–Yemen. Available from: http://www.climatestotravel.com/climate/yemen.
[34]	A. A. King, E. L. Ionides, M. Pascual, et al., Inapparent infections and cholera dynamics, Nature, 454 (2008), 877–880.
[35]	X. Wang, X. Q. Zhao and J. Wang, A cholera epidemic model in a spatiotemporally heterogeneous environment, J. Math. Anal. Appl., 468 (2018), 893–912.

Reader Comments

your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)