Modified Hermite Wavelet Method for the Transmission Dynamics of Monkeypox Virus Model

This paper presents the theoretical and numerical aspects of a mathematical model of the Monkeypox virus using the Modified Hermite Wavelet Collocation Method (HWCM). The model accounts for all interactions influencing the spread of the disease, which, like cowpox and smallpox, monkeypox is caused by the Monkeypox Virus (MPV) and is prevalent in isolated populations near tropical rainforests in West and Central Africa. The study analyzes the model using HWCM and fractional-order derivatives. An Operational Matrix of Integration (OMI) based on Hermite wavelets is constructed to reduce the Fractional Differential Equations (FDEs) to an algebraic system, which is then solved using the Newton–Raphson method to yield the unknown Hermite coefficients. Tables and Graphical results are provided to validate the theoretical findings. HWCM proves efficient, requiring only a few terms to achieve high accuracy even under nonlinear conditions. The method’s results are compared with those of the RK4 and NDSolver methods, demonstrating the effectiveness and precision of HWCM. The variation of dependent variables is analyzed by varying different parameters of the model.