A Fractional Order Hiv/Aids Model Using Caputo-Fabrizio Operator

Abstract

Background: HIV is a virus that is directed at destroying the human immune system thereby exposing the human body to the risk of been affected by other common illnesses and if it is not treated, it generates a more chronic illness called AIDS. Materials and Methods: In this paper, we employed the fixed-point theory in developing the uniqueness and existence of a solution of fractional order HIV/AIDS model having Caputo-Fabrizio operator. This approach adopted in this work is not conventional when solving biological models by fractional derivatives. Results: The results showed that the model has two equilibrium points namely, disease-free, and endemic equilibrium points, respectively. We showed conditions necessitating the existence of the endemic equilibrium point and showed that the disease-free equilibrium point is locally asymptotically stable. We also tested the stability of our solution using the iterative Laplace transform method on our model which was also shown stable agreeing with the disease-free equilibrium. Conclusions: Numerical simulations of our model showed clear comparison with our analytical results. The numerical solutions show that given fractional operator like the Caputo-Fabrizio operator, it is less noisy and plays a major role in making a precise decision and gives room (‘freedom’) to use data of specific patients as the model can be easily adjusted to accommodate this, as it a better fit for the patients’ data and provide meaningful predictions. Finally, the result showed the advantage of using fractional order derivative in the analysis of the dynamics of HIV/AIDS over the classical case.

Mathematical Modelling Approach of the Study of Ebola Virus Disease Transmission Dynamics in a Developing Country.

“…Even when the symptoms of the Ebola disease were no longer detectable in a patient's blood, the virus was still found present in breast milk. It was equally shown in some research works that the virus can be present in semen 40 days after the virus symptoms began 2021). For these reasons, people are encouraged to practice abstinence from both breastfeeding and unprotected sex immediately after recovering from Ebola virus disease (Bausch et al, 2007), 2021).…”

“…It was equally shown in some research works that the virus can be present in semen 40 days after the virus symptoms began 2021). For these reasons, people are encouraged to practice abstinence from both breastfeeding and unprotected sex immediately after recovering from Ebola virus disease (Bausch et al, 2007), 2021). When infected with Ebola disease, the symptoms of this disease may appear as from between two to twenty-one days.…”