Browsing by Author "Rezapour, Shahram"

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    A Study on Dynamics of CD4+ T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials
    (MDPI, 2022-04) Najafi, Hashem; Etemad, Sina; Patanarapeelert, Nichaphat; Asamoah, Joshua Kiddy K.; Rezapour, Shahram; Sitthiwirattham, Thanin; 0000-0002-7066-246X
    In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD4+ T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.
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    A theoretical and numerical analysis of a fractal–fractional two-strain model of meningitis
    (Elsevier, 2022-06) Rezapour, Shahram; Asamoah, Joshua Kiddy K.; Hussain, Azhar; Ahmad, Hijaz; Banerjee, Ramashis; Etemad, Sina; Botmart, Thongchai; 0000-0002-7066-246X
    Meningitis is an inflammation of the membranes that surround and protect the brain and spinal cord. Typically, the enlargement is caused by a bacterial or viral infection of the fluid around the brain and spinal cord. For many years, licensed vaccinations against meningococcal, pneumococcal, and Haemophilus influenzae diseases have been accessible. Vaccines are meant to protect against the most dangerous strains of these germs, which are known as serotypes or serogroups. There have been significant increases in strain coverage and vaccine availability throughout time, but there is no universal vaccine against these illnesses. In this study, we explore the mathematical features of a new six-compartmental fractal–fractional two-strain model of meningitis. With the use of compact functions and 𝜙 − 𝜓-contractions, we establish the existence of solutions. To study the unique solutions, we employ the Banach principle. On the basis of the Hyers-Ulam definition for the fractal– fractional two-strain model of meningitis, stable solutions are examined. From the numerical simulations, we notice that as the fractal–fractional order decreases, the number of infected individuals with strain 1 of meningitis decreases, while the number of infected individuals with strain 2 rises. This means that all serotypes or serogroups need to be controlled effectively for the disease to be closed up.
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    On the fractal-fractional Mittag-Leffler model of a COVID-19 and Zika Co-infection
    (Elsevier, 2023-11) Rezapour, Shahram; Asamoah, Joshua Kiddy K.; Etemad, Sina; Akgül, Ali; Avcı, İbrahim; Din, Sayed M. El; 0000-0002-7066-246X
    The World Health Organization declared COVID-19 a global pandemic in March 2020, which had a significant impact on global health and economies. There have been several Zika outbreaks in different regions such as Africa, Southeast Asia, and the Americas. Therefore, it is essential to study the dynamics of these two diseases, taking into account their memory and recurrence effects. A new fractal-fractional hybrid Mittag-Leffler model of COVID-19 and Zika co-dynamics is designed and studied to evaluate the effects of COVID-19 on Zika and vice-versa. The stability analysis of the local asymptotic type at disease-free equilibrium is conducted for the hybrid model. The existence of unique solutions to the model is established via some fixed point results. The fractal-fractional model is proved to be Hyers–Ulam stable. With the help of Newton polynomials, we obtain some numerical algorithms to approximate the solutions of the fractal-fractional hybrid Mittag-Leffler model graphically. The impact of fractional and fractal orders on the dynamics of each of the epidemiological classes is also assessed. In addition, empirical evidence from numerical simulations suggests that implementing measures to contain the transmission of the SARS-CoV-2 virus can significantly contribute to the reduction of co-infections involving the Zika virus. Therefore, it is imperative for healthcare systems to maintain a state of constant vigilance in order to detect any atypical patterns or probable occurrences of co-infections, particularly in areas where both diseases are widespread. Additionally, it is vital to consult the most recent directives provided by health authorities, as our comprehension of diseases may undergo advancements over the course of time.