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BACKGROUND AND OBJECTIVE: Hepatitis virus infections are affecting millions of people worldwide, causing death, disability, and considerable expenditure. Chronic infection with hepatitis C virus (HCV) can cause severe public health problems because of their high prevalence and poor long-term clinical outcomes. Thus a fractional-order epidemic model of the hepatitis C virus involving partial immunity under the influence of memory effect to know the transmission patterns and prevalence of HCV infection is studied. Investigating the transmission dynamics of HCV makes the issue more interesting. The HCV epidemic model and worldwide dynamics are examined in this study. Calculate the basic reproduction number for the HCV model using the next-generation matrix technique. We determine the model's global dynamics using reproduction numbers, the Lyapunov functional approach, and the Routh-Hurwitz criterion. The model's reproduction number shows how the disease progresses. METHODS: A fractional differential equation model of HCV infection has been created. Maximum relevant parameters, such as fractional power, HCV transmission rate, reproduction number, etc., influencing the dynamic process, have been incorporated. The model's numerical solutions are obtained using the fractional Adams method. Finally, numerical simulations support the theoretical conclusions, showing the great agreement between the two. RESULTS: In the fractional-order HCV infection model, the memory effect, which is not seen in the classical model, was shown on graphs so that disease dynamics and vector compartments could be seen. We found that the fractional-order HCV infection model has more stages of freedom than regular derivatives. Fractional-order derivations, which may be the best and most reliable, explained bodily approaches better than classical order. CONCLUSION: The current study modeled and analyzed a fractional-order HCV infection model. The current approach results in a much better understanding of HCV transmission in a population, which leads to important insights into its spread and control, such as better treatment dosage for different age groups, identifying the best control measure, improving health, prolonging life, reducing the risk of HCV transmission, and effectively increasing the quality of life of HCV patients. The creation of a fractional-order HCV infection model, which provides a better understanding of HCV transmission dynamics and leads to significant insights for better treatment dosages, identification of optimal control measures, and ultimately improvement of the quality of life for HCV patients, is the study's major outcome.
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This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton's method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.
