Mingfeng He

Fixation probabilities in evolutionary games with the Moran and Fermi processes.

An evolutionary dynamic model of 2×2 games with finite population of size N+M was built. Among these individuals, N individuals have the same update mechanism as that of the Moran process, while the other M individuals have the same update mechanism as that of the Fermi process. We obtain the balance equations of the fixation probability and analyze some concrete cases. In contrast with the results of neutral evolution, the fixation probability of a single co-operator with the same update mechanism as that of the Fermi process is higher. Besides, more co-operators with the update mechanism of the Fermi process lead to higher fixation probabilities when co-operators׳ quantity is the same.

Disease Control of Delay SEIR Model with Nonlinear Incidence Rate and Vertical Transmission

The aim of this paper is to develop two delayed SEIR epidemic models with nonlinear incidence rate, continuous treatment, and impulsive vaccination for a class of epidemic with latent period and vertical transition. For continuous treatment, we obtain a basic reproductive number ℜ 0 and prove the global stability by using the Lyapunov functional method. We obtain two thresholds ℜ* and ℜ ∗ for impulsive vaccination and prove that if ℜ* < 1, then the disease-free periodic solution is globally attractive and if ℜ ∗ > 1, then the disease is permanent by using the comparison theorem of impulsive differential equation. Numerical simulations indicate that pulse vaccination strategy or a longer latent period will make the population size infected by a disease decrease.

Modeling the Parasitic Filariasis Spread by Mosquito in Periodic Environment

In this paper a mosquito-borne parasitic infection model in periodic environment is considered. Threshold parameter R0 is given by linear next infection operator, which determined the dynamic behaviors of system. We obtain that when R0 < 1, the disease-free periodic solution is globally asymptotically stable and when R0 > 1 by Poincaré map we obtain that disease is uniformly persistent. Numerical simulations support the results and sensitivity analysis shows effects of parameters on R0, which provided references to seek optimal measures to control the transmission of lymphatic filariasis.

A moderate hatred of the rich mentality promotes cooperation in prisoner’s dilemma game:

Most current studies involving prisoner’s dilemma games are formulated under the assumption that participators are rational during collective interaction. Although irrationality in some patterns has been considered in the evolution, the effects brought about by the hatred of the rich mentality have never been investigated. Here, we introduce a cumulative reward-based rule where a player will adopt an irrational strategy which is expressed in defection in the game if the cumulative reward of the opponent exceeds the threshold controlled by a given parameter. Interestingly, despite irrational defection, such rules will result in the best environment for cooperator’s viability. In addition, we have demonstrated that irrationality in this form could be favorable for the average allocation of wealth in terms of Gini coefficient.

Temptation to Defect May Promote Cooperation in Prisoner’s Dilemma Game

In this paper, basing on the prisoner’s dilemma model proposed by M.A.Nowak, we present a model to research the action of temptation to defect in prison’s dilemma model. Firstly, we determine whether a player changes its strategy depends on a Fermi equation which is related to the payoffs of the player and its neighbors. If the player changes its strategy next time step, it will select the strategy adopted by the one who gets the highest payoff among its neighbors as its own strategy. Form the results we find that when four neighbors are considered, the density of cooperators will present a downtrend. Well, when eight neighbors are considered, the density of cooperators will decline at the beginning and increase suddenly afterwards. When twelve neighbors are considered, if the density of cooperators is reduced to zero, cooperation will appear again. Thus, the increase of temptation to defect may promote cooperation.

Stability Analysis of Hepatitis B Virus Model with Incomplete Immunization of HepB Vaccine

In this paper a HBV infection model with impulsive vaccination is considered. By using fixed point theorem and stroboscopic map we prove the existence of disease-free T-periodic solution. Also by comparative theorem of impulsive differential equation we get the global asymptotic stability of the disease-free periodic solution and permanence of the disease. Numerical simulations show the influence of parameters on the dynamics of HBV, which provided references for seeking optimal measures to control the transmission of HBV.