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<p>The present study employs a five-dimensional nonlinear mathematical model to investigate malaria transmission in situations where healthcare resources are limited. Firstly, the model’s well-posedness is guaranteed by ensuring the boundedness and non-negativity of the solution of the system. Then, the local and global stability analysis of different equilibria are discussed with the help of the driven basic reproduction number. Next, the occurrence conditions of transcritical bifurcation and Hopf-bifurcation are obtained. Finally, for the purpose of numerical simulation of the propose model, we develop a novel dynamically consistent second-order nonstandard finite difference (NSFD) technique by extending the Mickens’ methodology. We show that constructed NSFD method not only maintains the positivity property but also achieves second-order convergence. Theoretical findings and advantages of the NSFD method are validated through illustrative numerical simulations. The current approach has the potential to be extended for the development of second-order NSFD methods applicable to certain classes of nonlinear dynamical systems. In addition, the deterministic model is converted to its stochastic framework and using numerical simulation results of deterministic and stochastic models are compared. Finally, the model is validated using yearly malaria case data from the United Kingdom for the years 2002–2021.</p>

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A nonlinear malaria model under healthcare constraints: analysis of bifurcation, development of a second-order NSFD scheme, and stochastic comparison

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Tapan Sarkar,
  • Sanuwar Ahmed Choudhury,
  • Saduri Das

摘要

The present study employs a five-dimensional nonlinear mathematical model to investigate malaria transmission in situations where healthcare resources are limited. Firstly, the model’s well-posedness is guaranteed by ensuring the boundedness and non-negativity of the solution of the system. Then, the local and global stability analysis of different equilibria are discussed with the help of the driven basic reproduction number. Next, the occurrence conditions of transcritical bifurcation and Hopf-bifurcation are obtained. Finally, for the purpose of numerical simulation of the propose model, we develop a novel dynamically consistent second-order nonstandard finite difference (NSFD) technique by extending the Mickens’ methodology. We show that constructed NSFD method not only maintains the positivity property but also achieves second-order convergence. Theoretical findings and advantages of the NSFD method are validated through illustrative numerical simulations. The current approach has the potential to be extended for the development of second-order NSFD methods applicable to certain classes of nonlinear dynamical systems. In addition, the deterministic model is converted to its stochastic framework and using numerical simulation results of deterministic and stochastic models are compared. Finally, the model is validated using yearly malaria case data from the United Kingdom for the years 2002–2021.