Analysis of a HBV model with diffusion and time delay. (English) Zbl 1263.92024

Summary: This paper discusses a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.


92C60 Medical epidemiology
35B35 Stability in context of PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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