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Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

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Listed:
  • Ali, Javaid
  • Raza, Ali
  • Ahmed, Nauman
  • Ahmadian, Ali
  • Rafiq, Muhammad
  • Ferrara, Massimiliano

Abstract

This work presents a novel evolutionary computation-based Padé approximation (EPA) scheme for constructing a closed-form approximate solution of a nonlinear dynamical model of Covid-19 disease with a crowding effect that is a growing trend in epidemiological modeling. In the proposed framework of the EPA scheme, the crowding effect-driven system is transformed to an equivalent nonlinear global optimization problem by assimilating Padé rational functions. The initial conditions, boundedness, and positivity of the solution are dealt with as problem constraints. Keeping in view the complexity of formulated optimization problem, a hybrid of differential evolution (DE) and a convergent variant of the Nelder-Mead Simplex algorithm is also proposed to obtain a reliable, optimal solution. The comparison of the EPA scheme results reveals that optimization results of all formulated optimization problems for the Covid-19 model with crowding effect are better than those of several modern metaheuristics. EPA-based solutions of the Covid-19 model with crowding effect are in good agreement with those of a well-practiced nonstandard finite difference (NSFD) scheme. The proposed EPA scheme is less sensitive to step lengths and converges to true equilibrium points unconditionally.

Suggested Citation

  • Ali, Javaid & Raza, Ali & Ahmed, Nauman & Ahmadian, Ali & Rafiq, Muhammad & Ferrara, Massimiliano, 2021. "Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect," Operations Research Perspectives, Elsevier, vol. 8(C).
    • Handle: RePEc:eee:oprepe:v:8:y:2021:i:c:s2214716021000245
    DOI: 10.1016/j.orp.2021.100207
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    References listed on IDEAS

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    1. Mohammad Mehdi Rashidi & Mohammad Keimanesh, 2010. "Using Differential Transform Method and Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-14, April.
    2. Ullah, Saif & Khan, Muhammad Altaf, 2020. "Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Natee Panagant & Sujin Bureerat, 2014. "Solving Partial Differential Equations Using a New Differential Evolution Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, June.
    4. Javaid Ali & Muhammad Saeed & Muhammad Farhan Tabassam & Shaukat Iqbal, 2019. "Controlled showering optimization algorithm: an intelligent tool for decision making in global optimization," Computational and Mathematical Organization Theory, Springer, vol. 25(2), pages 132-164, June.
    5. Gupta, Vedika & Jain, Nikita & Katariya, Piyush & Kumar, Adarsh & Mohan, Senthilkumar & Ahmadian, Ali & Ferrara, Massimiliano, 2021. "An Emotion Care Model using Multimodal Textual Analysis on COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Mateescu, George Daniel, 2006. "On the Application of Genetic Algorithms to Differential Equations," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 3(2), pages 5-9, June.
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    1. Ghada Ali Basendwah & Nauman Raza & Javaid Ali, 2023. "Evolutionary Padé Approximation for Heat and Mass Transfer Analysis of Falkner–Skan Flow of a Bio-Convective Casson Fluid," Mathematics, MDPI, vol. 11(7), pages 1-25, March.

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