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We analyse a periodically-forced SIR model to investigate the influence of seasonality on the disease dynamics and we show that the condition on the basic reproduction number $mathcal{R}_0<1$ is not enough to guarantee the elimination of the disease. Using the theory of rank-one attractors, for an open subset in the space of parameters of the model for which $mathcal{R}_0<1$, the flow exhibits persistent strange attractors, producing infinitely many periodic and aperiodic patterns. Although numerical experiments have already suggested that periodically-forced SIR model may exhibit observable chaos, a rigorous proof was not given before. Our results agree well with the empirical belief that intense seasonality induces chaos. This should serve as a warning to all doing numerics (on epidemiological models) who deduce that the disease disappears merely because $mathcal{R}_0<1$.
This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic reproduction number
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system
In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then, for a qualit
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $delta$ of the network and the frequency $omega$ of the p
We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed in quarantine (SIQR model), considering that the flow of individuals