A Note on Solutions of the SIR Models of Epidemics Using HAM

Recently, Awawdeh et al. (2009) discussed the solutions of SIR epidemics model using homotopy analysis method. This comment points out some crucial flaws in (Awawdeh et al. 2009). Particularly, results presented in Figure 1 of the (Awawdeh et al. 2009) do not represent the 20 term solution of the considered problem as stated. The present paper also provides a new approach for solving SIR epidemics model using homotopy analysis method. The new approach is based on dividing the entire domain into subintervals. In each subinterval the three-term HAM solution is sufficient for obtaining accurate and convergent results. The comparison of the obtained solution using new approach is made with the numerical results and found in excellent agreement. 1. Introduction The authors in [1] have considered the classic SIR epidemic model for the homotopy analysis method (HAM) solution. The constant population in SIR model is divided into susceptible, infectious, and recovered classes [2, 3]. The expressions for the susceptible, infectious, and recovered population presented in [1] for five- and nine-term HAM solutions clearly indicate that, for , the initial population size is 20, 15, and 10, respectively. However, Figure 1 illustrates a different population size. The same analytic expressions for the susceptible, infectious, and recovered populations for the same problem are presented in the literature with Adomian decomposition method [4], variational iteration method [5], homotopy perturbation method [6], and differential transform method [7]. The graphical results in all the studies [4–7] reveal that the results are valid for small values of time and beyond that these analytic expressions fail to give results that can be compared with the existing numerical solutions. However, the authors in [1] obtained same expressions as presented in [4–7], but the graphical results are different from all these studies which are not possible. Thus Figure 1 present in [1] is not found through 20-term HAM solution. Figure 1: Plot for susceptible population when , , and . The objective of the present paper is to revisit the HAM solution for the nonlinear initial value problems considered by Awawdeh et al. [1] and to provide a HAM solution which agrees well with the numerical results already obtained for the same problem. For the accurate and convergent HAM solution valid for all ranges of time values, we propose a new approach. In this new approach the whole domain of the problem is divided into subintervals, and the HAM solution is evaluated separately in each subinterval. A