Actuarial review of models for describing and predicting the spread of HIV infection and AIDS

Haberman, Steven

doi:10.1017/s0020268100043122

Cited by 8 publications

(7 citation statements)

References 89 publications

(144 reference statements)

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“…Haberman [6] presented an excellent review of the basic approach to deterministic epidemic transmission models. We begin with simple models for the spread of HIV infection within a closed group of male homosexuals.…”

Section: Fundamentals Of Deterministic Epidemic Transmission Models; mentioning

confidence: 99%

“…The models may be adapted to deal with heterosexual spread in a two-sex population and with needle sharing associated with IV-drug abuse [6]. We start with a simple model for the spread of HIV infection within a closed male homosexual community and assume that the total population has a fixed size, n.…”

Section: Fundamentals Of Deterministic Epidemic Transmission Models; mentioning

confidence: 99%

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Modeling the Transmission Dynamics of HIV/AIDS epidemics: an introduction and a review.

Akpa

Oyejola

2010

J Infect Dev Ctries

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Introduction: One of the greatest causes of morbidity and mortality in the Sub-Saharan Africa, particularly among young adults, is HIV/AIDS. Many mathematical models have been suggested for describing the epidemiology as well as the epidemiological consequences of the epidemic. A review of some these models would aid researchers in applying them to better understand and control the incidence and distribution of the disease in their countries. Methodology: This study reviews some of the models proposed by various authors for describing the epidemiology as well as the epidemiological consequences of the HIV/AIDS epidemic and how some of them could be modified to suit the situations in other countries. We also discuss the limitations and the place of such models in the fight against the HIV epidemic. Results: A clear explanation of the premises and assumptions on which the models were based was reached by reviewing the models across different scenarios. Conclusion: Mathematical models have been very useful in HIV research, particularly for empirical studies on people living with HIV/AIDS (PLWHA). These models make predictions that generate questions of social and ethical interest.

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Section: Fundamentals Of Deterministic Epidemic Transmission Models; mentioning

confidence: 99%

Section: Fundamentals Of Deterministic Epidemic Transmission Models; mentioning

confidence: 99%

Modeling the Transmission Dynamics of HIV/AIDS epidemics: an introduction and a review.

Akpa

Oyejola

2010

J Infect Dev Ctries

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“…The Institute of Actuaries Working Party model is similar to many of the other mathematical models described in Haberman (1990). However, because of the emphasis on applying this model to assessing the effect of HIV and AIDS on life insurance underwriting, life insurance premiums and reserving (as well as permanent health insurance and pension provision), the focus of this actuarial model has been different.…”

Section: Institute Of Actuaries Aids Working Party Modelmentioning

confidence: 99%

“…It relies heavily on the early sections of Hoem (1988) and also on an excellent paper by Ramsay (1989) which explored similar themes for models of AIDS transmission, developed for the Society of Actuaries and being used in the United States of America. A full review of such transmission models is provided by Haberman (1990).…”

Section: Introductionmentioning

confidence: 99%

HIV, AIDS and the approximate calculation of life insurance functions, annuities and net premiums

Haberman¹

1992

J. Inst. Actuar.

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The paper presents an application of the Markov chain as a tool for the calculation of life contingencies functions (e.g. assurance, annuity, net premium, policy value functions) arising from a multi-state model which represents the transmission and development of HIV and AIDS. The transmission model advocated by the Institute of Actuaries AIDS Working Party is modified and simplified and then applied to derive explicit formulae for these standard life contingencies functions. This investigation allows a thorough review of the properties of these functions to be conducted and assists with the calculation of premiums and reserves in the presence of HIV and AIDS.

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“…The epidemiological models of HIV infections categorize each individual as susceptible or infected. Infected individuals are assumed to transmit HIV virus to susceptible individuals with the same transmission rate in the duration of disease [10,11]. It is also studied that host biological factors such as age, sex, genetic susceptibility, time since infection, and status of immune system may cause variation in infectiousness of infected individuals [12].…”

Section: Introductionmentioning

confidence: 99%

Between-host HIV model: stability analysis and solution using memetic computing

Ahmed¹,

Qureshi²,

Saleem³

et al. 2019

Turk J Elec Eng & Comp Sci

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HIV poses a great threat to humanity for two major reasons. First it attacks the immunity system of the body and second, it is epidemic in nature. Mathematical models of HIV have been instrumental in understanding and controlling the infection. In this paper, we solve the between host epidemic model of HIV, described by nonlinear coupled differential equations, by using memetic computing. Under this model, the sexually active population is divided into four classes and we investigate the transfer of individuals from one class to another. The solution consists of Bernstein polynomials whose parameters have been optimized by using differential evolution as global and sequential quadratic programming as local optimizer. Our second contribution is the stability analysis of this model. The disease-free equilibrium is stable while endemic equilibrium is unstable within the practical range of the values of parameters.

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Actuarial review of models for describing and predicting the spread of HIV infection and AIDS

Cited by 8 publications

References 89 publications

Modeling the Transmission Dynamics of HIV/AIDS epidemics: an introduction and a review.

Modeling the Transmission Dynamics of HIV/AIDS epidemics: an introduction and a review.

HIV, AIDS and the approximate calculation of life insurance functions, annuities and net premiums

Between-host HIV model: stability analysis and solution using memetic computing

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