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Long Term Combat of HIV/AIDS : An HIV ExpenseCushioning Effect [Government and Insurance

Industry Cost sharing Mechanism]

Baloi L. and Kgosimore M.

August 31, 2011

1 Background and information

HIV/AIDS discovered in the early 1980s has now established itself as a serious publichealth challenge requiring to be classified as a chronic disease. The disease is very ex-pensive once infected subjects develop Full Blown AIDS. Issues of economic melt-downhave compounded problems of funding for HIV treatment programmes. In various spheresthe current state of the epidemic and continued high levels of new infections on yearly

basis with resource-poor countries or countries with high level incidence and prevalencerates; the main question is can governments sustain the HIV/AIDS epidemic. Ironically,that questions seem to have an optimistic no. The follow-up question then is what otheralternatives methodologies or interventions can be put in place to mitigate against theeventual bleak future of sustaining the epidemic.

The proposed problem wishes to bring alternative approaches to planning, evaluation andmonitoring of the epidemic, in the context of economics and battle-field mathematicalmodels or predator-prey models. The approach considers the role of partnerships of gov-ernment, insurance service providers and the civic society in investing in public healthwith emphasis on HIV/AIDS, which has a significant bearing on socio-economic attributesof the society. The long term problem considers investment and recovery of monetary re-sources and reduction of man-lives. This can be achieved or realized in the long terminvestment prior to the development of the disease. The expense cushioning effect canbe achieved through investment in medical insurances.

The incubation period of HIV/AIDS is roughly 10 years. This long incubation periodallows for an accrual of necessary finances to fight the disease at a later stage. Our argu-ment is that if there is a national medical insurance the invested funds can later be used

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to fight the disease or avail anti-retroviral drugs. To visualize the problem a simplisticmodel using the pigeon hole principle can be envisioned and models as

Pn =

1 + r100

nP (1)

where P is the principal value (or initial value), r annual rate of investment, n durationof investment in years and Pn investment maturity value after n years.

2 Problem statement

We consider a SEIR model with three classes described as follows: A susceptible pop-

ulation (S), individuals in the class are free from infection and are at risk of acquiringinfection upon interaction with infected individuals; the asymptomatic HIV infected pop-ulation, (E), individuals in this class are infected with no clinical signs, infectious butthey may be unaware of their HIV status; the symptomatic infected population ( I) haveclinical signs and are highly infectious. Treatment of HIV usually start in this class lead-ing to a class of Treated individuals (T), which may eventually progress to the class orremovals. Treatment in a way plays a crucial role of delaying death; and full BlownAIDS population (R) usually referred to as removal class, are mostly bed-ridden and playminimal role in the transmission dynamics of the disease.

2.1 Model assumptions

The problem relaxed other related costs such those of hospitalizations, development ofdrug resistance due to lack of adherence and other effects like drug toxicity.

3 Methodology

3.1 Cost measurement criterion

1. The cost of anti-retroviral drugs

2. Reduction of progression to death (or reduction in disease related rates)

The main aim of provision of drugs is reduce the level of infectiousness (form of preventionmechanism against those at risk) and reduce the disease related deaths (prolonged life-expectancy). We therefore need to formulate multiple control functions that maximizethese benefits against the high cost of anti-retroviral drugs. We propose a control functionof the form

j =1

0bu2dt + (1 b)x(t) (2)

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The study discusses control problems (i) Jc describing the cost of ARV control func-tion (ii) Jd describing the reduction in diseases related deaths control function and (iii)Jp describing the preventive mechanism control function due reduced level of infectious-ness. So that we consider a mathematical problem j = Jc Jd Jp which over a longtime would not be economically viable with increased number of infections and cost ofARVs. We visualize this problem in the context Laws of supply and demand and othereconomies of scale, raw materials, over time for hospital personnel and labour implicationsalso compound to the cost factor blowing it further. Other, anticipated challenges canarise from viral rebound or drug resistance leading to acquisition of new and expensivedrug combinations. It is notable to have an ever increasing control functions with noupper bounds and optimal solutions as the functions will not be integrable in all spaces.

However smoothing functions involving fourier series summations may be usedto overcome discontinuities of the functions. This description is consistent withcurrent situations.

3.2 Solution approach

The methods of solution will involve determination of model equilibria or study the dif-ferent scenarios emanating from (a) adequate resources and disease outcome (b) effectsof inadequate monetary resources on the severity of the epidemic as influenced by dis-ease incidence, prevalence and deaths and (c) evolution of drug resistance as a result ofinadequate drugs and money. We wish to explore different approaches such as

1. Application of battle modelling approaches with investments representing para-trooper actions

2. Predator-prey models with HIV/AIDS preying on both resources and funds

3. Application of stochastic models

4 Objectives

The main objective of the study is to determine an optimal strategy to sustain the epi-demic and effectively reduce the proportion dying of the disease to a lower predeterminedvalue ( < ).

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