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In this paper, we present stochastic methods for computation of influenza transmission models. First, SEIR type deterministic epidemiological models are revisited and stochastic modeling for those models are introduced. The main motivation of our work is to present computational methods of the stochastic epidemic models. In particular, the moment closure method (MCM) is developed for some influenza models and compared with the results under the standard stochastic simulation algorithm (SSA). All epidemic outcomes including the peak size, the peak timing and the final epidemic size of both methods are in a good agreement, however, the MCM has reduced the computational time and costs significantly. Next, the MCM has been employed to model the 2009 H1N1 influenza transmission dynamics in South Korea. The influenza outcomes are compared under the standard deterministic approach and the stochastic approach (MCM). Our results show that there is a considerable discrepancy between the results of stochastic and deterministic models especially when a small number of infective individuals is present initially. Lastly, we investigate the effectiveness of control policies such as vaccination and antiviral treatment under various scenarios. [ABSTRACT FROM AUTHOR]

Currently, more than one million children suffer from hand, foot and mouth disease (HFMD) every year in China. And there are no effective vaccines or antiviral drugs specifically targeted HFMD. In this paper, a two stage-structured model is constructed to fit the HFMD data from 2009 to 2014 in China and obtain its optimal parameter values by the Chi-square test of statistical inference. Using the parameter values obtained can precisely and reliably forecast the clinical cases. The basic reproduction numbers for each year are more than unit, which suggests that HFMD will persist in China under the current conditions. Sensitivity analysis of the basic reproduction number is conducted to evaluate the effectiveness of HFMD control measures. Using Pontryagins maximum principle, we derive the necessary conditions for optimal control of HFMD. Further, the impact of combinations of the strategies on HFMD transmission is investigated. Finally, we find out the most cost-effective strategy though carrying out cost-effectiveness analysis. [ABSTRACT FROM AUTHOR]

• Two numerical methods are developed for solving the fractional-order HIV-1 infection model of CD4 + T-cells. • Two method (Bessel matrix method and Bessel quasilinearization method) are based on the novel Bessel polynomials. • Error and convergence analysis are studied. • Numerical applications and comparisons show that methods are effective. • In the comparison of the two methods used, the Bessel-QLM method gives better results. In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD 4 + T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method. [ABSTRACT FROM AUTHOR]

Abstract: The fast point-to-group information sharing process within an enterprise network also exposes information to more severe virus attacks. On the other hand, a relative large number of virus attacks may result in psychological effects of inhibition for the network end-users. In this paper, a nonlinear force of infection function for e-SEIR model is presented to study the crowding and psychological effects in network virus prevalence. By carrying out a global analysis of the stability of both the virus-free and endemic equilibrium, this work reveals how the crowding and psychological effects have impacts on network virus propagation process. Furthermore, analysis and simulation results show some managerial insights that are helpful for the practice of antivirus in information sharing networks. [Copyright &y& Elsevier]