Efficient Solution of Fractional-Order SIR Epidemic Model of Childhood Diseases With Optimal Homotopy Asymptotic Method

Abstract

In providing an accurate approximate analytical solution to the non-linear system of fractional-order susceptible-infected-recovered epidemic model (FOSIREM) of childhood disease has been a challenge because no norm guarantees the convergence of the infinite series solution. We compute an accurate approximate analytical solution using the optimal homotopy asymptotic method (OHAM). The fractional differential equations operator (FDEO) is given as conformable derivative operator (CDO). We show the basic idea of the proposed method, the CDO sense, equilibrium points, local asymptotic stability, reproduction number, and the convergence analysis of the proposed method. Numerical results and comparisons with other approximate analytical solutions are given to validate the efficiency of the method. The proposed method speedily converges to the exact solution as the fractional-order derivative approaches 1 proved an excellent tool for solving and predicting the model.

Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates

“…Thereby, the instantaneous behavior of the dynamic system can be depicted with the effect of past accumulations. In this regard, many mathematical models, including integer and fractional order, have been created in the literature for the detailed analysis of various diseases such as cancer cells [3][4][5], varicella zoster virus [6], COVID-19 [7][8][9], plant disease [10], diabetes [11], prey-predator model [12], Nipah virus [13], childhood diseases [14], and hepatitis B [15]. Additionally, several studies have also been conducted regarding fractional derivative applications in various fields, such as optimal control [16,17], fixed point theory [18][19][20], chaotic systems [21], and heat flow [22].…”

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

“…Hashimet al 17 considered OHAM-2 for resolving numerous simulations of first-order fuzzy fractional IVPs. Olumide et al 18 studied the efficient result of the fractional-order SIR epidemic exemplary of childhood diseases with OHAM-2. Ahsanet al 19 presented a numerical result of a scheme of fuzzy fractional order Volterra integro-differential equation utilizing OHAM-2.…”