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\iteman{ZMATH 1233.92068}
\itemau{Dong, Fu'an; Wei, Minjian; Yu, Bin}
\itemti{Theory and simulation analysis of a discrete-time SISV epidemic model.}
\itemso{J. Northwest Norm. Univ., Nat. Sci. 47, No. 1, 12-16 (2011).}
\itemab
Summary: Probability is introduced to formulate the death of individuals, recovery of infected individuals, loss immunity of vaccinal individuals and incidence of epidemic diseases. Discrete-time SISV epidemic models with nonlinear incidence rate are established. In case of the total population dynamics being a compensator, the threshold determining its dynamical behavior is found. Below the threshold the disease-free equilibrium is locally asymptotically stable and simulations show that in the model backward bifurcations at certain parameter values occur. Above the threshold the model is uniformly persistent. In the case that the total population dynamics is overcompensatory, simulations show that while the total population dynamics undergoes a period-doubling bifurcation route to chaos, the susceptive population dynamics, infective population dynamics and vaccinal population dynamics also undergo a period-doubling bifurcation route to chaos.
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\itemcc{92D30 34D20 65C20}
\itemut{dynamical behavior; equilibrium; stability}
\itemli{}
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