American Institute of Mathematical Sciences

Advanced
January  1995, 1(1): 35-57. doi: 10.3934/dcds.1995.1.35

Diffusive epidemic models with spatial and age dependent heterogeneity

W. E. Fitzgibbon 1, , M.E. Parrott 2, and  Glenn Webb 3,

1. 

Department of Mathematics, University of Houston, Houston, Texas, 77204-3476, United States
2. 

University of South Florida, United States
3. 

Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, United States

Received  July 1994 Published  December 1994

An epidemic model is analyzed which allows for the spatial spread of individuals within a geographical region and the incubation of the disease within infected individuals. The spatial spread of the disease is modelled by diffusion processes. The incubation period of infectives is modelled by infection-age structure. Results are established which provide qualitative prediction of the development of the epidemic in terms of spatially dependent and age dependent parameters.
Keywords: semilinear parabolic systems., diffusion processes, disease within infected individuals, infection-age structure.
Mathematics Subject Classification: 35K10, 92B0.
Citation: W. E. Fitzgibbon, M.E. Parrott, Glenn Webb. Diffusive epidemic models with spatial and age dependent heterogeneity. Discrete & Continuous Dynamical Systems - A, 1995, 1 (1) : 35-57. doi: 10.3934/dcds.1995.1.35
[1]

Suxia Zhang, Xiaxia Xu. A mathematical model for hepatitis B with infection-age structure. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1329-1346. doi: 10.3934/dcdsb.2016.21.1329
[2]

Cameron Browne. Immune response in virus model structured by cell infection-age. Mathematical Biosciences & Engineering, 2016, 13 (5) : 887-909. doi: 10.3934/mbe.2016022
[3]

Yanxia Dang, Zhipeng Qiu, Xuezhi Li. Competitive exclusion in an infection-age structured vector-host epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (4) : 901-931. doi: 10.3934/mbe.2017048
[4]

C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381-400. doi: 10.3934/mbe.2015008
[5]

Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson. An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells. Mathematical Biosciences & Engineering, 2004, 1 (2) : 267-288. doi: 10.3934/mbe.2004.1.267
[6]

Yueding Yuan, Zhiming Guo, Moxun Tang. A nonlocal diffusion population model with age structure and Dirichlet boundary condition. Communications on Pure & Applied Analysis, 2015, 14 (5) : 2095-2115. doi: 10.3934/cpaa.2015.14.2095
[7]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
[8]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017
[9]

Jie Lou, Tommaso Ruggeri, Claudio Tebaldi. Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior. Mathematical Biosciences & Engineering, 2006, 3 (2) : 313-324. doi: 10.3934/mbe.2006.3.313
[10]

Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915
[11]

Brooke L. Hollingsworth, R.E. Showalter. Semilinear degenerate parabolic systems and distributed capacitance models. Discrete & Continuous Dynamical Systems - A, 1995, 1 (1) : 59-76. doi: 10.3934/dcds.1995.1.59
[12]

Jinliang Wang, Xiu Dong. Analysis of an HIV infection model incorporating latency age and infection age. Mathematical Biosciences & Engineering, 2018, 15 (3) : 569-594. doi: 10.3934/mbe.2018026
[13]

Cameron J. Browne, Sergei S. Pilyugin. Global analysis of age-structured within-host virus model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 1999-2017. doi: 10.3934/dcdsb.2013.18.1999
[14]

Yilong Li, Shigui Ruan, Dongmei Xiao. The Within-Host dynamics of malaria infection with immune response. Mathematical Biosciences & Engineering, 2011, 8 (4) : 999-1018. doi: 10.3934/mbe.2011.8.999
[15]

Fred Brauer. A model for an SI disease in an age - structured population. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257
[16]

Liming Wang. A passivity-based stability criterion for reaction diffusion systems with interconnected structure. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 303-323. doi: 10.3934/dcdsb.2012.17.303
[17]

Felipe Wallison Chaves-Silva, Sergio Guerrero, Jean Pierre Puel. Controllability of fast diffusion coupled parabolic systems. Mathematical Control & Related Fields, 2014, 4 (4) : 465-479. doi: 10.3934/mcrf.2014.4.465
[18]

P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
[19]

Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155
[20]

Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences