In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced in the CTL response term to represent time required to stimulate the immune system. Based on fractional Laplace transform, some conditions on stability and Hopf bifurcation are derived for the model. The analysis shows that the fractional-order with time-delay can effectively enrich the dynamics and strengthen the stability condition of fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations.
Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.
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