Research Article Open Access

Mathematical Analysis of the Non Linear Epidemic Model

Laid Chahrazed-Rahmani Fouad Lazhar1
  • 1 University Mentouri, Algeria

Abstract

Classical epidemic models assume that the size of the total population is constant. More recent models consider a population size variable to take into account a longer period with death and disease causing reduced reproductive. The model contains a disease-free equilibrium and one or multiple equilibria are endemic. The stability of a disease-free status equilibrium and the existence of other nontrivial equilibria can be determined by the ratio called the basic reproductive number, which quantifies the number of secondary infections arise from a simple put infected in a population of sensitive. First, the local stability of the infection-free equilibrium and endemic equilibrium were analyzed, respectively. Second, the endemic equilibrium was formulated in terms of the incidence rate and local asymptotic stability. Finally we applied the adomian decomposition method to the system Epidemiologic. This method yields an analytical solution in terms of convergent infinite power series.

Journal of Mathematics and Statistics
Volume 8 No. 2, 2012, 258-263

DOI: https://doi.org/10.3844/jmssp.2012.258.263

Submitted On: 24 December 2011 Published On: 19 June 2012

How to Cite: Lazhar, L. C. F. (2012). Mathematical Analysis of the Non Linear Epidemic Model. Journal of Mathematics and Statistics, 8(2), 258-263. https://doi.org/10.3844/jmssp.2012.258.263

  • 3,084 Views
  • 2,482 Downloads
  • 1 Citations

Download

Keywords

  • Adomian decomposition method
  • basic reproduction number
  • model epidemiology
  • locally asymptotically stability
  • global stability