Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385.

Primary: 37G15, 37G35; Secondary: 39A11, 92B05.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Periodically forced discrete-time SIS epidemic model with disease induced mortality

1. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205
2. Department of Mathematics, Howard University, Washington, DC 20059

We use a periodically forced SIS epidemic model with disease induced mortality to study the combined effects of seasonal trends and death on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, $R_0$, for predicting disease dynamics in periodic environments. Typically, $R_0<1$ implies disease extinction. However, in the presence of disease induced mortality, we extend the results of Franke and Yakubu to periodic environments and show that a small number of infectives can drive an otherwise persistent population with $R_0>1$ to extinction. Furthermore, we obtain conditions for the persistence of the total population. In addition, we use the Beverton-Holt recruitment function to show that the infective population exhibits period-doubling bifurcations route to chaos where the disease-free susceptible population lives on a 2-cycle (non-chaotic) attractor.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Epidemics; infectives; periodic environments; susceptibles.

Citation: John E. Franke, Abdul-Aziz Yakubu. Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385

 

This article has been cited by

  • 1. Zhidong Teng, Lei Wang, Linfei Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Mathematical Methods in the Applied Sciences, 2015, 38, 18, 4741, 10.1002/mma.3389
  • 2. Qiaoling Chen, Zhidong Teng, Lei Wang, Haijun Jiang, The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence, Nonlinear Dynamics, 2013, 71, 1-2, 55, 10.1007/s11071-012-0641-6
  • 3. Najat Ziyadi, Abdul-Aziz Yakubu, Predator-induced and mating limitation-induced Allee effects in a discrete-time SIMS epidemic model, Computers & Mathematics with Applications, 2013, 66, 11, 2196, 10.1016/j.camwa.2013.08.002
  • 4. Yueli Luo, Shujing Gao, Dehui Xie, Yanfei Dai, A discrete plant disease model with roguing and replanting, Advances in Difference Equations, 2015, 2015, 1, 10.1186/s13662-014-0332-3
  • 5. Xiaolin Fan, Lei Wang, Zhidong Teng, Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence, Advances in Difference Equations, 2016, 2016, 1, 10.1186/s13662-016-0846-y
  • 6. Najat Ziyadi, Abdul-Aziz Yakubu, , Mathematical Methods and Models in Biomedicine, 2013, Chapter 15, 411, 10.1007/978-1-4614-4178-6_15

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved