Global dynamics of a differential susceptibility model

Razvan, M. R ; Sharif University of Technology | 2012

587 Viewed
  1. Type of Document: Article
  2. DOI: 10.1142/S179352451100188X
  3. Publisher: 2012
  4. Abstract:
  5. An SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals has been analyzed. We prove that all the solutions tend to the equilibria of the system. Then we use the Poincaré Index theorem to determine the number of the rest points and their stability properties. It has been shown that bistability occurs for suitable values of the involved parameters. We use the perturbations of the pitchfork bifurcation points to give examples of all possible dynamics of the system. Some numerical examples of bistability and hysteresis behavior of the system has been also provided
  6. Keywords:
  7. Bifurcation ; Differential susceptibility ; Disease-free equilibrium ; Endemic equilibrium ; Epidemiological model ; Poincaré index
  8. Source: International Journal of Biomathematics ; Volume 5, Issue 5 , September , 2012 ; 17935245 (ISSN)
  9. URL: http://www.worldscientific.com/doi/abs/10.1142/S179352451100188X