DINAMIKA DUA JENIS INFLUENZA DENGAN ISOLASI DAN CROSS-IMMUNITY PARSIAL

Abstract

The time evolution of the influenza A virus is linked to a nonfixed landscape driven by interactions between hosts and competing influenza strains. Herd-immunity, cross im munity, and age-structure are among the factors that have been shown to support strain coexistence. In this study, we put two influenza strains under various levels of (interfe rence) competition. In general, this model have two kinds of equilibria state. The two kinds of equilibria of interest are those in which the disease is absent (a disease free equili brium) and those in which the disease is present (endemic). The presence of two endemic equilibria is found analytically. Furthermore, the equilibrium state of system is investi gated its stability. The stability of equilibrium system in the absence of infection is estab lished via basic reproduction number  for each strain and all of strain. It show that when  for , both strains die out. Furthermore, isolation periods and cross-immunity levels pertaining to the influenza virus lead to periodic epidemic outbreaks (the existence of sustained oscillations) in this system. These predictions are established via Hopf-bifurcation theory.

Keywords: bifurcation, coexistence, cross-immunity, influenza, isolation, multiple strains, oscillations, stability