TRANSMISSION DYNAMICS OF HIV/AIDS WITH OPTIMAL CONTROL IN THE PRESENCE OF CAREFREE SUSCEPTIBLES AND TREATMENT

BIOMAT 2011 ◽  
2012 ◽  
pp. 131-152 ◽  
Author(s):  
K. O. OKOSUN ◽  
O. D. MAKINDE ◽  
G. J. ABIODUN
Keyword(s):  
Optimal Control ◽  
Transmission Dynamics ◽  
Hiv Aids

scholarly journals Parameter-dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Francis Mugabi ◽  
Joseph Mugisha ◽  
Betty Nannyonga ◽  
Henry Kasumba ◽  
Margaret Tusiime
Keyword(s):  
Optimal Control ◽  
Deterministic Model ◽  
Foot And Mouth Disease ◽  
Decay Rates ◽  
Mouth Disease ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Optimality System ◽  
Foot And Mouth ◽  
Environmental Decontamination

AbstractThe problem of foot and mouth disease (FMD) is of serious concern to the livestock sector in most nations, especially in developing countries. This paper presents the formulation and analysis of a deterministic model for the transmission dynamics of FMD through a contaminated environment. It is shown that the key parameters that drive the transmission of FMD in a contaminated environment are the shedding, transmission, and decay rates of the virus. Using numerical results, it is depicted that the host-to-host route is more severe than the environmental-to-host route. The model is then transformed into an optimal control problem. Using the Pontryagin’s Maximum Principle, the optimality system is determined. Utilizing a gradient type algorithm with projection, the optimality system is solved for three control strategies: optimal use of vaccination, environmental decontamination, and a combination of vaccination and environmental decontamination. Results show that a combination of vaccination and environmental decontamination is the most optimal strategy. These results indicate that if vaccination and environmental decontamination are used optimally during an outbreak, then FMD transmission can be controlled. Future studies focusing on the control measures for the transmission of FMD in a contaminated environment should aim at reducing the transmission and the shedding rates, while increasing the decay rate.

scholarly journals Optimal control for variable order fractional HIV/AIDS and malaria mathematical models with multi-time delay

2020 ◽  
Vol 59 (5) ◽  
pp. 3149-3162 ◽  
Author(s):  
N.H. Sweilam ◽  
S.M. AL-Mekhlafi ◽  
Z.N. Mohammed ◽  
D. Baleanu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Mathematical Models ◽  
Variable Order ◽  
Hiv Aids

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 Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baba Seidu ◽  
Oluwole D. Makinde
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Nonlinear Dynamical ◽  
Basic Model ◽  
Hiv Aids

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number,R0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated whenR0<1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

scholarly journals Optimal control of HIV/AIDS dynamic: Education and treatment

2014 ◽  
Author(s):  
Amiru Sule ◽  
Farah Aini Abdullah
Keyword(s):  
Optimal Control ◽  
Hiv Aids

scholarly journals OPTIMAL CONTROL OF A SEX‐STRUCTURED HIV/AIDS MODEL WITH CONDOM USE

2009 ◽  
Vol 14 (4) ◽  
pp. 483-494 ◽  
Author(s):  
Gesham Magombedze ◽  
Zindoga Mukandavire ◽  
Christinah Chiyaka ◽  
Godfrey Musuka
Keyword(s):  
Optimal Control ◽  
Condom Use ◽  
Optimal Control Theory ◽  
Intervention Strategy ◽  
Hiv Incidence ◽  
Aids Model ◽  
Condom Usage ◽  
Simulation Results ◽  
Objective Functional ◽  
Hiv Aids

Optimal control theory is applied to a sex‐structured HIV/AIDS model with condom use as an intervention strategy. An objective functional to maximise condom use in a population and minimise cases of infectious HIV is adopted. The optimal control is characterised and solved numerically. Simulation results suggest that high percentage of condom usage is associated with reduced HIV incidence, while high costs of condom usage campaigns reduces the percentage condom usage. Targeting issuance of condoms to infectious individuals enables reduction of condom usage campaign costs, hence ensures high percentage of condom usage.

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