Free terminal time optimal control of a fractional-order model for the HIV/AIDS epidemic

2021 ◽  
Author(s):  
Mohsen Jafari ◽  
Hossein Kheiri
Keyword(s):  
Optimal Control ◽  
State Control ◽  
Aids Epidemic ◽  
Terminal Time ◽  
Model Control ◽  
Time Optimal ◽  
Control Terminal ◽  
Exposure Prophylaxis ◽  
Free Terminal Time ◽  
Hiv Aids

In this paper, we present a fractional model for the HIV/AIDS epidemic and incorporate into the model control parameters of pre-exposure prophylaxis (PrEP), behavioral change and antiretroviral therapy (ART) aimed at controlling the spread of diseases. We prove the local and global asymptotic stability of disease-free and endemic equilibria of the model. We present a general fractional optimal control problem (FOCP) with free terminal time and develop the Adapted Forward-Backward Sweep method for numerical solving of the FOCP. Necessary conditions for a state/control/terminal time triplet to be optimal are obtained. The results show that the use of all controls increases the life expectancy of HIV-treated patients with ART and remarkably increases the number of people undergoing PrEP and changing their sexual habits. Also, when the derivative order [Formula: see text] ([Formula: see text]) limits to 1, the value of optimal terminal time increases while the value of objective functional decreases.

scholarly journals Free terminal time optimal control problem for the treatment of HIV infection

2016 ◽  
Vol 6 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Amine Hamdache ◽  
Smahane Saadi ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Hiv Infection ◽  
Control Problem ◽  
Time Optimal Control ◽  
Optimal Controls ◽  
Terminal Time ◽  
Time Optimal ◽  
Time Optimal Control Problem ◽  
Free Terminal Time

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. The optimal treatment duration and the optimal medications amount are considered. The main objective of this study is to be able to maximize the benet based on number of healthy CD4+ T-cells and CTL immune cells and to minimize the infection level and the overall treatment cost while optimizing the duration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employedto provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.

scholarly journals Dynamic analysis and optimal control of a three-age-class HIV/AIDS epidemic model in China

2020 ◽  
Vol 25 (9) ◽  
pp. 3491-3521
Author(s):  
Hongyong Zhao ◽  
◽  
Peng Wu ◽  
Shigui Ruan ◽  
Keyword(s):  
Optimal Control ◽  
Dynamic Analysis ◽  
Epidemic Model ◽  
Age Class ◽  
Aids Epidemic ◽  
Hiv Aids

scholarly journals Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

2021 ◽  
Vol 136 (1) ◽  
Author(s):  
Adnane Boukhouima ◽  
El Mehdi Lotfi ◽  
Marouane Mahrouf ◽  
Silvério Rosa ◽  
Delfim F. M. Torres ◽  
...  
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Aids Epidemic ◽  
General Incidence Rate ◽  
With Memory ◽  
Hiv Aids

scholarly journals Fractional order optimal control problems with free terminal time

2014 ◽  
Vol 10 (2) ◽  
pp. 363-381 ◽  
Author(s):  
Shakoor Pooseh ◽  
◽  
Ricardo Almeida ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Terminal Time ◽  
Free Terminal Time
Sign in / Sign up

Export Citation Format

Share Document