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In this paper, we introduce a numerical and analytical study of the HIV‐1 infection of CD4+ T‐cells conformable fractional mathematical model. This model is studied analytically by Kudryashov and modified Kudryashov methods and numerically by finite difference method. A comparison between the results of the analytical and numerical methods is investigated. We also give some figures that show how accurate the solutions will be obtained from analytical and numerical methods. [ABSTRACT FROM AUTHOR]

In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number ℛ0 is given through mathematical analysis, which is a threshold to determine whether or not the disease spreads. Secondly, the locally and globally asymptotical stability of the disease‐free equilibrium point and the endemic equilibrium point are investigated by using Lyapunov functions and Kirchhoff's matrix tree theorem. If ℛ0<1, the disease‐free equilibrium is globally asymptotically stable and the disease will die out. If ℛ0>1, the endemic equilibrium is globally asymptotically stable. Thirdly, an optimal control problem is established by taking slaughter rate and cure rate as control variables. Finally, numerical simulations are given to demonstrate the main results. [ABSTRACT FROM AUTHOR]