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

Diffusive epidemic models with spatial and age dependent heterogeneity

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.
Citation: W. E. Fitzgibbon, M.E. Parrott, Glenn Webb. Diffusive epidemic models with spatial and age dependent heterogeneity. Discrete and Continuous Dynamical Systems, 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 and 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]

Huizi Yang, Zhanwen Yang, Shengqiang Liu. Numerical threshold of linearly implicit Euler method for nonlinear infection-age SIR models. Discrete and Continuous Dynamical Systems - B, 2023, 28 (1) : 70-92. doi: 10.3934/dcdsb.2022067

[5]

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

[6]

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

[7]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure and 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 and Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017

[9]

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

[10]

Connell McCluskey. Lyapunov functions for disease models with immigration of infected hosts. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4479-4491. doi: 10.3934/dcdsb.2020296

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

Sérgio S. Rodrigues. Semiglobal exponential stabilization of nonautonomous semilinear parabolic-like systems. Evolution Equations and Control Theory, 2020, 9 (3) : 635-672. doi: 10.3934/eect.2020027

[19]

Qi Wang, Yanyan Zhang. Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities. Communications on Pure and Applied Analysis, 2022, 21 (3) : 797-816. doi: 10.3934/cpaa.2021199

[20]

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

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (255)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]