Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results

Dynamical Analysis of a Fractional Order HIV/AIDS Model

This article discusses a dynamical analysis of the fractional-order model of HIV/AIDS. Biologically, the rate of subpopulation growth also depends on all previous conditions/memory effects. The dependency of the growth of subpopulations on the past conditions is considered by applying fractional derivatives. The model is assumed to consist of susceptible, HIV infected, HIV infected with treatment, resistance, and AIDS. The fractional-order model of HIV/AIDS with Caputo fractional-order derivative operators is constructed and then, the dynamical analysis is performed to determine the equilibrium points, local stability and global stability of the equilibrium points. The dynamical analysis results show that the model has two equilibrium points, namely the disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable when the basic reproduction number is less than one. The endemic equilibrium point exists if the basic reproduction number is more than one and is globally asymptotically stable unconditionally. To illustrate the dynamical analysis, we perform some numerical simulation using the Predictor-Corrector method. Numerical simulation results support the analytical results

Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in the Caputo sense. This model takes into account the relationship between Tuberculosis, HIV/AIDS, and diabetes and differentiates resistance cases into MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant tuberculosis). We present the basic results associated with the model and study the behavior of the disease-free equilibrium points in the different sub-populations, TB-Only, TB-HIV/AIDS, and TB-Diabetes. We performed computational simulations for different fractional orders (α-values) using an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among the results obtained, we have that the MDR-TB cases in all sub-populations decrease at the beginning of the study for the different α-values. In XDR-TB cases in the TB-Only sub-population, there is a decrease in the number of cases. XDR-TB cases in the TB-HIV/AIDS sub-population have differentiated behavior depending on α. This knowledge helps to design an effective control strategy. The XDR-TB cases in diabetics increased throughout the study period and outperformed all resistant compartments for the different α-values. We recommend special attention to the control of this compartment due to this growth

Antiretroviral therapy of HIV infection using a novel optimal type-2 fuzzy control strategy

Abstract The human immunodeficiency virus (HIV), as one of the most hazardous viruses, causes destructive effects on the human bodies' immune system. Hence, an immense body of research has focused on developing antiretroviral therapies for HIV infection. In the current study, we propose a new control technique for a fractional-order HIV infection model. Firstly, a fractional model of the HIV model is investigated, and the importance of the fractional-order derivative in the modeling of the system is shown. Afterward, a type-2 fuzzy logic controller is proposed for antiretroviral therapy of HIV infection. The developed control scheme consists of two individual controllers and an aggregator. The optimal aggregator modifies the output of each individual controller. Simulations for two different strategies are conducted. In the first strategy, only reverse transcriptase inhibitor (RTI) is used, and the superiority of the proposed controller over a conventional fuzzy controller is demonstrated. Lastly, in the second strategy, both RTI and protease inhibitors (PI) are used simultaneously. In this case, an optimal type-2 fuzzy aggregator is also proposed to modify the output of the individual controllers based on optimal rules. Simulations results demonstrate the appropriate performance of the designed control scheme for the uncertain system