A study on fractional HIV‐AIDs transmission model with awareness effect

The model of care of people living with HIV/AIDS (PLWHA) has shifted from hospital care to community home-based care (CHBC) because of shortage of space in hospitals and lack of resources. We evaluate the costs and benefits of home-based care and other HIV/AIDS intervention strategies in Zimbabwe, using an interdisciplinary approach which weaves together the techniques of an epidemic transmission model and economic evaluation concepts. The intervention strategies considered are voluntary counselling and testing (VCT), VCT combined with hospitalization (H), VCT combined with CHBC, and all the interventions implemented concurrently. The results of the study indicate that implementing all the strategies concurrently is the most cost-effective, a result which also agrees with the epidemiological model. Our results also show that the effectiveness of a strategy in the epidemiological model does not necessarily imply cost-effectiveness of the strategy and behaviour change, modelled by the parameters p and m, that accompanied the strategies, influencing both the cost-effectiveness of an intervention strategy and dynamics of the epidemic. This study shows that interdisciplinary collaborations can help in improving the accuracy of predictions of the course and cost of the epidemic and help policy makers in implementing the correct strategies.

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Mathematical analysis of a delayed HIV/AIDS model with treatment and vertical transmission

Open Journal of Mathematical Sciences ◽

10.30538/oms2021.0151 ◽

2021 ◽

Vol 5 (1) ◽

pp. 128-146

Author(s):

Gratien Twagirumukiza ◽

◽

Edouard Singirankabo ◽

Keyword(s):

Public Health ◽

Vertical Transmission ◽

Death Rate ◽

Reproduction Number ◽

Transmission Model ◽

Asymptomatic Group ◽

Death Rates ◽

Infected People ◽

Epidemic Diseases ◽

Hiv Aids

None can underestimate the importance of mathematical modelling for their role in clarifying dynamics of epidemic diseases. They can project the progress of the disease and demonstrate the result of the epidemic to public health in order to take precautions. HIV attracts global attention due to rising death rates and economic burdens and many other consequences that it leaves behind. Up to date, there is no medicine and vaccine of HIV/AIDS but still many researches are conducted in order to see how to mitigate this epidemic and reduce the death rate or increase the life expectancy of those who are infected. A delayed HIV/AIDS treatment and vertical transmission model has been investigated. The model took into account both infected people from the symptomatics group and asymptomatic group to join AIDS group. We considered that a child can be infected from the mother to an embryo, fetus or childbirth. Those who are infected, it will take them some time to get mature and spread the disease. By using mathematical model, reproduction number, positivity, boundedness, and stability analysis were determined. The results showed that the model is much productive if time delay is considered.

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A Class Age-Structured HIV/AIDS Model with Impulsive Drug-Treatment Strategy

Discrete Dynamics in Nature and Society ◽

10.1155/2010/758745 ◽

2010 ◽

Vol 2010 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Helong Liu ◽

Lianbing Li

Keyword(s):

Drug Treatment ◽

Antiretroviral Treatment ◽

Impulsive Differential Equations ◽

The State ◽

Transmission Model ◽

Effective Vaccine ◽

Infection Age ◽

Aids Epidemic ◽

Age Structured ◽

Hiv Aids

We formulate an HIV/AIDS transmission model that considers the dependence of HIV/AIDS progress on infection age (the time since infection), disease age (the time elapsed since the onset), and impulsive antiretroviral treatment. Since no effective vaccine is available for HIV/AIDS, our impulsive disease-control strategy is targeted at infected individuals (I control). Thus the model only includes infective class and AIDS class: infected population is the state at birth, and AIDS population is not the state at birth. Assuming the theoretical strategy can provide HIV testing for risk population groups every years and immediate antiretroviral treatment for HIV-positive people. The action is approximated by impulsive differential equations. We demonstrate the effect of the impulsive drug treatment and show that there exists a globally stable infection-free state when the impulsive period and drug-treatment proportion satisfy . This result shows that the prevention effects can drive HIV/AIDS epidemic towards to elimination.

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