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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]

In ecosystem, the most critical issue is the extinction and persistence of population. For this reason, various deterministic and stochastic models have been studied in the past decades. However, the effect of transitions which is caused by either internal or external environmental noise has given less attention. In this work, we introduce a robust and an efficient numerical scheme based on Legendre spectral collocation method (LSCM) to explore the asymptomatic behavior of stochastic influenza avian model. We consider the model in which both birds and human population are exposed class, while for the human population, the asymptomatic class is also considered, taking into account that the asymptomatic human beings may get re‐infected and migrate to symptomatic class. A fragmented treatment gives more consideration as they relocate symptomatic individuals towards the asymptomatic class. A generation approach is utilized to figure out the essential propagation number (called reproduction number) denoted by R0. For R0 < 1, the system is asymptotically stable locally and has an ailment disease free equilibrium (DFE) and may have up to five endemic equilibria. Our simulations results recommend that the pace of complete predominance of influenza will be high, if all the individuals show symptoms upon infection and experience a deficient treatment. Further, the predominance pace of influenza is low, if all the individuals first move to symptomatic class and then treated effectively. An average rate of total prevalence is secured when more individuals upon disease move towards asymptomatic class. Our numerical simulations justified the theoretical results. [ABSTRACT FROM AUTHOR]

We present a nonlinear fractional order epidemic model to investigate the spreading dynamical behavior of the avian influenza. The population of the model contains susceptible individuals, asymptomatic but infective latent individuals, and infective individuals. We first establish the existence, uniqueness, nonnegativity, and positive invariance of the solution, then we study the reproduction number of the model and the stability of the disease‐free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative ν. In terms of epidemics, this suggests that varying ν induces a change in the avian's epidemic status. Furthermore, we derive the sufficient conditions for the existence and the stability of the endemic equilibrium. Finally, we carry out some numerical simulations to validate the analytical results. We find from simulations that the solution of the fractional order model tends to a stationary state over a longer period of time with decreasing the value of the fractional derivative, and the size of epidemic decreases with decreasing ν. [ABSTRACT FROM AUTHOR]

In 2013, in mainland China, a novel avian influenza A(H7N9) virus began to infect humans, followed by the annual outbreaks, and had aroused severe fatality in the infected humans. After introducing the statistical characteristics including the geographical distributions of the outbreaks, a SEV‐SIRS eco‐epidemiological model is established and analyzed. In this model, the factor of virus in environment is incorporated into the model as a class; the vaccine measure in poultry is taken into account in purpose of assessing its control effect in 2017 in China; the nonmonotonic contact function is adopted to characterize the psychosocial effect. The stability of disease‐free equilibrium point (DFE) is obtained by the threshold theory; the stability of the endemic equilibrium point is gotten by the Bendixson criterion based on the geometric approach. Sensitivity analyses of system parameters indicate that the measure of vaccination in poultry can play its role but only when the vaccine rate is more than 98% can the disease control effect be effectively exerted, and the virus in environment is an extremely sensitive factor in the disease transmission and the epidemic control. [ABSTRACT FROM AUTHOR]