In this work we consider the general stochastic SIR (Susceptible - Infected - Removed) epidemic model with the transition intensity q(S,I),(S−1,I+1) = βg(S)I, where g(x) is a function density dependent. An approximation of the final size by a diffusion process is given. Finally, I introduce some numerical simulation graphics to illustrate the main result.
In this work, the Chebyshev spectral-collocation method is applied to obtain approximate solution for some types of linear parabolic partial integro–differential equations (PPIDEs). In the first approach, we convert our equation into two coupled Volterra integral equations of the second kind by using a proper transformation. In the second approach, the integration in the resulting equations are approximated by replacing the integrand by its interpolating polynomials in terms of the Chebyshev polynomials instead of using the approximation by Gauss quadrature rules. After approximation a linear algebraic system were raised, then it tested by the conditional number. Finally, some numerical examples are included to illustrate the validity and applicability of the proposed technique.
The paper presents two methods for solving the fractional Fornberg-Whitham (FFW) equation. Based on the peaked solutions of FW equation, suppose the solution’s variable-separated form, and the FFW equation is transformed into a constant fractional differential equation (FDE). To solve the transformed equation, first, the fractional variational iteration method (FVIM) is used. Secondly, the undetermined coefficient method is used to expand the solution of the constant FDE. The expansion is based on the Generalized Taylor formula. Also the solutions are yielded for FFW. It should be pointed out that two cases of the order of fractional derivative between 1 and 2 and that between 0 and 1 are discussed respectively for the transformed FDE. Last, we give two numerical examples by using the two presented methods. The results show that the results agree well by both two proposed methods, and the two methods are high efficient in solving FFW.
Every organisation has an objective to optimise the utility function of its available operational assets. For commercial vehicle transport operators, the goal is to operate the vehicles for as long as they can make net contribution to the organisation’s corporate objective. Hence, when these vehicles are replaced becomes an issue for strategic decision making. Unfortunately many of the commercial bus transport companies lack the skill to undertake the required empirical evaluation necessary to provide objective data and information for making the vehicle replacement decisions. This study was therefore an effort to bridge this gap in knowledge. Only two out of the fourteen transporter companies of interest operating in Benin City, Edo State, Nigeria agreed to provide the required data for the study which covered the period 2008 to 2013 and for Toyota brand of buses only. The data was subjected to backward recursive dynamic programming analysis. The results showed that the four years fixed-age vehicle replacement policy employed by commercial bus transport companies in Benin City was optimum only for the Toyota high roof types of buses. The study thus recommends that commercial vehicle owners/operators should endeavour to keep reliable, relevant and up to records of their vehicles. While it is advocated that adequate and continuous training of key staff on equipment replacement should also be encouraged, operators of mass-transit systems can seek the assistance of Operations Research experts in order to enhance their decisions regarding vehicle replacement policies.
This paper deals with the problem of delay-dependent robust H∞ ï¬ltering for switched T-S fuzzy systems with interval time-varying delays and parameter uncertainties. This represents a novelty in this research domain since to the best of our knowledge there is no paper, in the literature, dealing with the delay-dependent robust H∞ ï¬ltering for switched T-S fuzzy systems time-varying delays. Our attention is focused on the design of a full order filter that guarantees the filtering error system to be robustly stable with a prescribed H∞ performance. By choosing a new Lyapunov function and using the convexity property, new sufficient conditions are derived for stability robustness of the filtering error systems and are expressed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the effectiveness and the superiority of the proposed design methods.
In this paper the study of unsteady hydromagnectic free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium was conducted. The temperature is assumed to be oscillating with time, also the effects of hall-current is taken in to account. The solution of velocity, temperature and concentration profiles have been obtained. The effects of various parameters on temperature, concentration primary and secondary velocity profiles were presented graphically.
Cloud computing is an evolutionary approach that completely changes how computing services are produced, priced and delivered. Cloud computing allows to access services that reside in a distant datacenter, other than local computers. Resource provisioning is the key process in cloud computing. The Virtual Machine (VM) is a software implementation of a machine that executes programs like a physical machine. Two stage scheduling is a novel approach in cloud computing. In this case a job may request two virtual machines in sequence to complete their needs. This paper presents a novel two stage scheduling algorithm to schedule the given job requests in cloud environment by extending Johnson’s Scheduling algorithm. Simulation results show that this algorithm reduces average waiting time and total elapsed time when compared to other scheduling algorithms.