ABSTRACT:We proposed a mathematical model of infectious disease dynamics. The model is a system of first order ordinary differential equations. The population is partitioned into three compartments of Susceptible ) (t S , Infected ) (t I and Recovered ) (t R . Two equilibria states exist: the disease-free equilibrium which is locally asymptotically stable if Ro < 1 and unstable if Ro > 1. Numerical simulation of the model shows that an increase in vaccination leads to low disease prevalence in a population.
In this study, Akbari-Ganji’s Method (AGM) was applied to solve Volterra Integro-Differential Difference Equations (VIDDE) using Legendre polynomials as basis functions. Here, a trial solution function of unknown constants that conform with the differential equations together with the initial conditions were assumed and substituted into the equations under consideration. The unknown coefficients are solved for using the new proposed approach, AGM which principally involves the application of the boundary conditions on successive derivatives and integrals of the problem to obtain a system of equations. The system of equation is solved using any appropriate computer software, Maple 18. Some examples were solved and the results compared to the exact solutions.
This paper presents an analysis of PSIuIeTR type model, which are used to study the transmission dynamics of typhoid fever diseases in a population. Basic idea of typhoid fever disease transmission using compartmental modeling is discussed. Differential Transformation Method (DTM) is discussed in detail, which is used to compute the series solution of the non-linear system of differential equation governing the model equations. The validity of the (DTM) in solving the proposed model is established by classical fourth-order Runge-Kutta method which is implemented in Maple 18. Graphical results confirm that (DTM) is in good agreement with RK-4 and this produced correctly same behaviour of the model, thus validating the efficiency and accuracy of (DTM) in finding the series solution of an epidemic model.
In this study, we present a collocation computational technique for solving Volterra-Fredholm Integro-Differential Equations (VFIDEs) via fourth kind Chebyshev polynomials as basis functions. The method assumed an approximate solution by means of the fourth kind Chebyshev polynomials, which were then substituted into the Volterra-Fredholm Integro-Differential Equations (VFIDEs) under consideration. Thereafter, the resulting equation is collocated at equally spaced points, which results in a system of linear algebraic equations with the unknown Chebyshev coefficients. The system of equations is then solved using the matrix inversion approach to obtain the unknown constants. The unknown constants are then substituted into the assumed approximate solution to obtain the required approximate solution.To test for the accuracy and efficiency of the scheme, six numerical examples were solved, and the results obtained show the method performs excellently compared to the results in the literature. Also, tables are used to outline the methods accuracy and efficiency.
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