Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 11
327
Views
1
CrossRef citations to date
0
Altmetric
Research Article

A partially degenerate reaction–diffusion cholera model with temporal and spatial heterogeneity

&
Pages 3167-3184 | Received 17 Apr 2021, Accepted 16 Mar 2022, Published online: 31 Mar 2022

References

  • Hartley DM, Morris JG Jr, Smith DL. Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics? PLoS Med. 2006;3:63–69.
  • Mukandavire Z, Liao S, Wang J, et al. Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe. Proc Natl Acad Sci USA. 2011;108:8767–8772.
  • World Health Organization (WHO) web page. Available from: https://www.who.int/health-topics/cholera#tab=tab_1
  • Capasso V, Paveri-Fontana SL. A mathematical model for the 1973 cholera epidemic in the European Mediterranean region. Rev Epidemiol Sante. 1979;27:121–132.
  • Wang X, Wang F-B. Impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment. J Math Anal Appl. 2019;480:Article ID 123407.
  • van den Driessche P, Shuai Z, Brauer F. Dynamics of an age-of-infection cholera model. Math Biosci Eng. 2013;10:1335–1349.
  • Yang J, Modnak C, Wang J. Dynamical analysis and optimal control simulation for an age-structured cholera transmission model. J Franklin Inst. 2019;356:8438–8467.
  • Shuai Z, van den Driessche P. Global dynamics of cholera models with differential infectivity. Math Biosci. 2011;234:118–126.
  • Tien JH, Earn DJD. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bull Math Biol. 2010;72:1506–1533.
  • Sun G-Q, Xie J-H, Huang S-H, et al. Transmission dynamics of cholera: mathematical modeling and control strategies. Commun Nonlinear Sci Numer Simul. 2017;45:235–244.
  • Sisodiya OS, Misra OP, Dhar J. Dynamics of cholera epidemics with impulsive vaccination and disinfection. Math Biosci. 2018;298:46–57.
  • Shuai Z, Tien JH, van den Driessche P. Cholera models with hyperinfectivity and temporary immunity. Bull Math Biol. 2012;74:2423–2445.
  • Bai N, Song C, Xu R. Mathematical analysis and application of a cholera transmission model with waning vaccine-induced immunity. Nonlinear Anal Real World Appl. 2021;58:Article ID 103232.
  • Zhang L, Wang Z-C, Zhang Y. Dynamics of a reaction–diffusion waterborne pathogen model with direct and indirect transmission. Comput Math Appl. 2016;72:202–215.
  • Wang J, Wang J. Analysis of a reaction–diffusion cholera model with distinct dispersal rates in the human population. J Dyn Differ Equ. 2021;33:549–575.
  • Wang X, Zhao X-Q, Wang J. A cholera epidemic model in a spatiotemporally heterogeneous environment. J Math Anal Appl. 2018;468:893–912.
  • Morillon M, De Pina JJ, Husser JA, et al. Djibouti, histoire de deux épidémies de choléra: 1993–1994. Bull Soc Path Ex. 1998;91:407–411.
  • Lawoyin TO, Ogunbodede NA, Olumide EAA, et al. Outbreak of cholera in Ibadan, Nigeria. Eur J Epidemiol. 1999;15:367–370.
  • Codeço CT. Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infect Dis. 2001;1:1.
  • Sanches RP, Ferreira CP, Kraenkel RA. The role of immunity and seasonality in cholera epidemics. Bull Math Biol. 2011;73:2916–2931.
  • Posny D, Wang J. Modelling cholera in periodic environments. J Biol Dyn. 2014;8:1–19.
  • Yang T, Zhang L. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete Contin Dyn Syst Ser B. 2019;24:6771–6782.
  • Martin RH, Smith HL. Abstract functional differential equations and reaction–diffusion systems. Trans Am Math Soc. 1990;321:1–44.
  • Li H, Peng R, Wang Z. On a diffusive dusceptible-infected-susceptible epidemic model with mass action mechanism and birth-death effect: analysis, simulations, and comparison with other mechanisms. SIAM J Appl Math. 2018;78:2129–2153.
  • Peng R, Zhao X-Q. A reaction–diffusion SIS epidemic model in a time-periodic environment. Nonlinearity. 2012;25:1451–1471.
  • Wu Y, Zou X. Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates. J Differ Equ. 2018;264:4989–5024.
  • Hale JK. Asymptotic behavior of dissipative systems. Providence: American Mathematical Society; 1988.
  • Liang X, Zhang L, Zhao X-Q. The principal eigenvalue for degenerate periodic reaction–diffusion systems. SIAM J Math Anal. 2017;49:3603–3636.
  • Thieme HR. Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J Appl Math. 2009;70:188–211.
  • Bacaër N, Guernaoui S. The epidemic threshold of vector-borne diseases with seasonality. J Math Biol. 2006;53:421–436.
  • Zhao X-Q. Basic reproduction ratios for periodic compartmental models with time delay. J Dyn Differ Equ. 2017;29:67–82.
  • Yu X, Zhao X-Q. A periodic reaction–advection–diffusion model for a stream population. J Differ Equ. 2015;258:3037–3062.
  • Zhang L, Wang Z-C, Zhao X-Q. Threshold dynamics of a time periodic reaction–diffusion epidemic model with latent period. J Differ Equ. 2015;258:3011–3036.
  • Zhao X-Q. Dynamical systems in population biology. 2nd ed. New York: Springer; 2017.
  • Magal P, Zhao X-Q. Global attractors and steady states for uniformly persistent dynamical systems. SIAM J Math Anal. 2005;37:251–275.
  • Bai Z, Peng R, Zhao X-Q. A reaction–diffusion malaria model with seasonality and incubation period. J Math Biol. 2018;77:201–228.
  • Zhang L, Wang S-M. A time-periodic and reaction–diffusion dengue fever model with extrinsic incubation period and crowding effects. Nonlinear Anal Real World Appl. 2020;51:Article ID 102988.
  • Liang X, Zhang L, Zhao X-Q. Basic reproduction ratios for periodic abstract functional differential equations (with application to a spatial model for Lyme disease). J Dyn Differ Equ. 2019;31:1247–1278.
  • Allen LJS, Bolker BM, Lou Y, et al. Asymptotic profiles of the steady states for an SIS epidemic reaction–diffusion model. Discrete Contin Dyn Syst. 2008;21:1–20.
  • Pang D, Xiao Y, Zhao X-Q. A cross-infection model with diffusive environmental bacteria. J Math Anal Appl. 2022;505:Article ID 125637.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.