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Background <p>Schistosomiasis is a parasitic disease. It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites. Schistosomiasis is the second most parasitic disease globally, so investigating its prevention and treatment is crucial.</p> Methods <p>This paper aims to suggest a time-fractional model of schistosomiasis disease (T-FMSD) in the sense of the Caputo operator. The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis (<i>S</i><sub><i>h</i></sub>(<i>t</i>)), those infected with the infection (<i>I</i><sub><i>h</i></sub>(<i>t</i>)), those recovering from the disease (<i>R</i>(<i>t</i>)), susceptible snails with and without schistosomiasis infection, respectively shown by <i>I</i><sub><i>v</i></sub>(<i>t</i>) and <i>S</i><sub><i>v</i></sub>(<i>t</i>). We use a new basis function, generalized Bernoulli polynomials, for the approximate solution of T-FMSD. The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.</p> Results <p>The existence and uniqueness of the solution, and the convergence analysis of the model are established. The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.</p> Conclusions <p>The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission. The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.</p>

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Optimal study of schistosomiasis in humans with environmental transmission via fractional order mathematical model

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Z. Avazzadeh,
  • H. Hassani,
  • A. Bayati Eshkaftaki,
  • M. J. Ebadi,
  • S. Mehrabi

摘要

Background

Schistosomiasis is a parasitic disease. It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites. Schistosomiasis is the second most parasitic disease globally, so investigating its prevention and treatment is crucial.

Methods

This paper aims to suggest a time-fractional model of schistosomiasis disease (T-FMSD) in the sense of the Caputo operator. The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis (Sh(t)), those infected with the infection (Ih(t)), those recovering from the disease (R(t)), susceptible snails with and without schistosomiasis infection, respectively shown by Iv(t) and Sv(t). We use a new basis function, generalized Bernoulli polynomials, for the approximate solution of T-FMSD. The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.

Results

The existence and uniqueness of the solution, and the convergence analysis of the model are established. The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.

Conclusions

The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission. The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.