Series solution of epidemic model

The present paper is concerned with the approximate analytic series solution of the epidemic model. In place of the traditional numerical, perturbation or asymtotic methods, Laplace-Adomian decomposition method (LADM) is employed.To demonstrate the effort of the LADM an epidemic model, which has been worked on recently, has been solved. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Furthermore the results are compared with Fouth Order Runge Method and residual error. After examining the results, we see that LADM is a powerful method for obtaining aproximate solutions to epidemic model.Publisher's Versio

Implementation of Adomian Decomposition Method for Maize Streak Virus Disease Model to Reduce the Contamination Rate in Maize Plant

              In this paper, the Maize Streak Virus disease model which involves the Maize and the Homopteran population is considered. This system of the differential equation is analytically solved by using Adomian Decomposition Method. The analytical results are compared with numerical simulation by assuming certain values for the parameter. Further, the demolishing and contamination rate of contagious and receptive homopteran on receptive and contagious Maize plant  parameters are analyzed to reduce the contamination rate. In addition, the death rates of contagious maize, receptive homopteran and contagious homopteran  are also discussed to remove the contagious population and make them free from Maize Streak Virus

Numerical Solution of SIR Model using Differential Transformation Method and Variational Iteration Method

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Seir Model of Seasonal Epidemic Diseases using HAM

SEIR mathematical model of childhood diseases measles, chickenpox, mumps, rubella incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. Driven by seasonality these diseases are characterized by annual oscillations with variable contact rate which is a periodic function of time in years. Homotopy Analysis Method (HAM) is considered in this paper to obtain a semi analytic approximate solution of non-linear simultaneous differential equations. Mathematica is used to carry out the computations. Results established through graphs show the validity and potential of HAM for amplitude of variation greater than zero. Also, when it is equal to zero both HAM and Runge-Kutta method graphs are compared

The first diffusion of the Covid-19 outbreak in Northern Italy: an analysis based on a simplified version of the SIR model

Abstract In this paper an analysis of the first diffusion of the Covid-19 outbreak occurred in late February 2020 in Northern Italy is presented. In order to study the time evolution of the epidemic it was decided to analyze in particular as the most relevant variable the number of hospitalized people, considered as the less biased proxy of the real number of infected people. An approximate solution of the infected equation was found from a simplified version of the SIR model. This solution was used as a tool for the calculation of the basic reproduction number R 0 in the early phase of the epidemic for the most affected Northern Italian regions (Piedmont, Lombardy, Veneto and Emilia), giving values of R 0 ranging from 2.2 to 3.1. Finally, a theoretical formulation of the infection rate is proposed, introducing a new parameter, the infection length, characteristic of the disease

An Accurate Analytical-Numerical Iterative Method for the Susceptible-Infected-Recovered Epidemic Models

We consider Susceptible-Infected-Recovered (SIR) models of infectious disease spread without and with vital dynamics. We recall some existing analytical approximate iterative methods for solving these models. We observe that all these methods solve the models accurately only for points close to the initialisation. These methods produce inaccurate, and even, unrealistic solutions to the SIR models if the time domain is sufficiently large. In this paper, our research objective is to propose an analytical-numerical iterative method, which is able to solve the SIR models accurately on the whole domain. The research method used is quantitative mathematical modelling with simulation. By implementing this analytical-numerical iterative method into a finite number of small consecutive subintervals of the domain, our research results show that the proposed method produces accurate solutions to the SIR models on the whole domain

The solution of fractional order epidemic model by implicit Adams methods

We consider the numerical solution of the fractional order epidemic model on long time-intervals of a non-fatal disease in a population. Under real-life initial conditions the problem needs to be treated by means of an implicit numerical scheme. Here we consider the use of implicit fractional linear multistep methods of Adams type. Numerical results are presented