Abstract
The discrete-time epidemic model is investigated, which is obtained using the Euler method. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos. The numerical simulations, including bifurcation diagrams and computation of Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors.
Highlights
Epidemic models have been widely used in different forms for studying epidemiological processes such as the spread of HIV [1], SARS [2], and influenza [3]
It is well known that dynamical systems with simple dynamical behavior in the constant parameter case display very complex behaviors including chaos when they are periodically perturbed [4, 5]
We have found that more attention is paid to the discrete-time epidemic models
Summary
Epidemic models have been widely used in different forms for studying epidemiological processes such as the spread of HIV [1], SARS [2], and influenza [3]. The continuous-time epidemic models have been widely investigated in many articles (e.g., [6,7,8,9,10] and the references cited therein). Daily treatments are frequently done for some infections, such as the group of those being responsible for the common cold, which do not confer any long lasting immunity. Such infections do not have a recovered state and individuals become susceptible again after infection.
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