A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

Abstract

Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractionalorder model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0, 1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adamstype predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach.

An Investigation on Analytical Properties of Delayed Fractional Order HIV Model: A Case Study

“…It is therefore reasonable to try to use a fractional compartmental system to observe the mechanism of the spread of diseases in epidemiological models. Biological models of fractional order have gained much attention in recent times which are more consistent for natural phenomena than integer-order systems that aid the characterization of dynamic systems such as memory property and fractional order system inherits some interesting properties from the integer order system [24,25,26,27,28,29,30,31,32,33].…”

Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two‐sex population

“…For future work, the proposed SNSFD can be executed to the complicated stochastic diffusion and stochastic delay epidemic models. Moreover, in the extension of the stochastic fractional order dynamical system [7,[29][30][31][32], the proposed numerical analysis of this work might also be used. Our future plan is to construct an authentic numerical scheme for the fractional order stochastic epidemic model for different diseases model.…”

“…India started to produce discounted HIV drugs for the under developed countries, some other pharmaceutical companies also sympathise for the reduction of HIV drugs prices. Developing countries are allowed to formulate inclusive medicines to fight against health crises such as HIV World Trade Organisation in November [6,7].…”

Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy

“…The distance of memory effect indicates the history of disease spread. Thus, memory effects on the spread of an infectious disease can be investigated using fractional derivatives [8][9][10][11][12][13].…”