Abstract
HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes in the current decade. These operators provide better dynamics of a mathematical model because these are the generalization of integer and fractional-order operators. This paper aims to study the dynamics of the HIV model during primary infection by fractal-fractional Atangana–Baleanu (AB) operators. The sufficient conditions for the existence and uniqueness of the solution of the proposed model under the AB operator are derived via fixed point theory. The numerical scheme is presented by using the Adams–Bashforth method. Numerical results are demonstrated for different fractal and fractional orders to see the effect of fractional order and fractal dimension on the dynamics of HIV and CD4+ T-cells during primary infection.
Highlights
Over the past few decades, the field of mathematical modeling of the physical process has gained considerable attention from scientists and investigators
Many mathematical models were built to study the understanding of many infectious diseases and to follow certain precautions to save a community from excessive loss
We show the impact of fractal and fractional order on the dynamics of HIV infection and its association with immune cells
Summary
Over the past few decades, the field of mathematical modeling of the physical process has gained considerable attention from scientists and investigators. We point out that mathematical models are important tools for studying many physical and biological science dynamic problems [1, 2]. In literature [1], computational solutions of the HIV-1 infection of the CD4+ T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy are presented. Ahmad et al studied the model describing the tumor and its relation with immune cells under the AB fractal-fractional operators [17]. Literature [18] has demonstrated the dynamics of the dengue infection model via fractal-fractional operators which are best fitted with real data. We use more generalized operators to model HIV infections and their association with immune cells. We show the impact of fractal and fractional order on the dynamics of HIV infection and its association with immune cells.
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