رشد اقتصادی و بیماری در مدل OLG: مطالعه موردی HIV / AIDS

The aim of this paper is to provide an analysis of the impact of investment in health-policies on economic development. In order to do this, it is vital to bear in mind the fact that long-term economic growth is characterized by the interaction between the physical aspects of capital dynamics and the disease level in a developing country which lacks a financial market. The OLG model will be used in our analysis. Notice that the level of investment in health policies and disease management are one of the key variables of the model. It is, therefore, interesting to observe that an increase in capital may have either a direct or indirect impact on the stationary disease level and lead to effective prevention and disease control.

A study carried out by the World Health Organization in 2001, clearly demonstrated that AIDS, malaria, and tuberculosis are diseases with the highest mortality rates. In the year 2000 alone, these diseases were responsible for more than 6 million deaths. Since 1981, the devastating ravage of Immunodeficiency Syndrome (HIV/AIDS), one of history's most deadly pandemics, has caused the deaths of more than 25 million people. If we focus our attention, merely, upon the dramatic consequences of these three highly-infectious diseases, it can be clearly observed that they have affected entire regions and countries. According to the UNAIDS and WHO's report (2008) the pandemic is still progressing at an alarming rate: “The number of people living with HIV worldwide continued to grow in 2008, reaching an estimated 33.4 million [31.1 million–35.8 million]. The total number of people living with the virus in 2008 was more than 20% higher than the number in 2000, and the prevalence was roughly threefold higher than in 1990.”, p.7. Effectively, since the beginning of the epidemic, nearly 60 million people have contracted HIV/AIDS, and 25 millions of those have perished. Recent epidemiological trends (UNAIDS Global Report, 2012) would seem to suggest that Sub-Saharan Africa suffers most of the disease burden. Representing over 2/3 (69%) of all people living with HIV and nearly 3/4 (70%) of AIDS-related deaths in 2011, Sub-Saharan Africa remains the hardest-hit region on a global level. In 2011, an estimated 1.8 million people living in this region while the number of people acquiring HIV infection in 2001 was equal to 2.4 million. Over 14 million children lost either one parent or became orphans due to AIDS-related mortality in each of the countries where HIV was present in more than 10% of the adult population. With 26% of the adult population affected by AIDS, Swaziland is the most severely affected country worldwide (UNAIDS, 2012). Economic underdevelopment is also a determining factor and largely responsible for the ravaging effects of the epidemic (e.g. The World Health Report, 2008). The very nature, widespread transmission and long-lasting effects of this disease account for the negative economic repercussions. From micro-economic viewpoint, Sachs (2005), noted that the destruction which HIV/AIDS causes in society can be compared to the ravages it causes in the human organism. It attacks the core of society as a whole, affecting people from all social backgrounds – men, women, breadwinners – those who live and protect the entire community are severely affected. In families, the direct cost of HIV/AIDS can be measured through loss of human life and the loss of employment due to the deadly implications of the disease. Needless to say, the very fact that Aids eradicates both individuals and families implies that it will also have dreadful repercussions on the nation's economy. Effective prevention and disease control, at an individual level is essential in halting and reversing the spread of HIV/AIDS. Prevention efforts would appear to be hampered since HIV/AIDS alters the agent's future expectations. An increased mortality rate, and a decline in life expectancy do not encourage investment and savings in the most heavily affected countries. From an overall point of view, HIV/AIDS can lead to reduced economic growth. According to Bonnel (2000), the causality between economic growth and disease is complex: “As shown by the previous system of equations the relations between HIV/AIDS and economic development are complex, particularly because of reverse causality. While HIV/AIDS reduces economic growth, economic growth can increase or decrease the spread of the HIV epidemic. On one hand, economic development can slow down the spread of the HIV epidemic. On the other hand, the process of economic development can facilitate the spread of the HIV epidemic.” p.4. Governments of developing countries are responding with large-scale preventive measures in the field of healthcare and disease management to protect future generations and ensure stable economic growth. Indeed, the Government may modify the intertemporal allocation of resources. Thus pensions are funded directly by the savings, or by the Government who imposes transfers between generations indirectly. More recently, the overlapping generations model has a new field of application in the field of health economics. This model is particularly adapted in the study of consequences of the economic policy on the evolution of the economy. Also this setup allows us to examine in depth the allocation of resources between generations. With the assumption of uncertain life expectancy due to an epidemiological shock, this model allows us to study the interactions between long term economic growth and disease evolution. Indeed, the economic costs of disease are considerable especially in developing countries (Bloom and Canning, 2006 and Pritchett and Summers, 1996). More, on the microeconomic level, the OLG model integrates behavior and incentives of agents in terms of prevention and investment. Demographic, disease affects in particular the structure of mortality and morbidity with consequences on dimensions microeconomic and macroeconomic developments. The intensification of disease can result in a reduction of the stock of physical capital as the factory, means of transportation… To our knowledge, this choice of modeling from generations of agents incorporating a disease is especially presented by Chakraborty (2004, 2007), Momota et al. (2005) assuming that agents can be infected and die prematurely. Preventive behavior change plays an important role in reducing the prevalence of the disease. In this context, the preventive behavior of agents in the neo-classical theory is studied with the probability of survival from one period to another. The probability is determined endogenously. It depends particularly on the agent's health investment and the disease level. In the end, the dynamics of the economy is modified by the presence of the disease. Recent empirical studies highlight the complexity of the links between wealth and disease (Bloom and Canning, 2006 and Pritchett and Summers, 1996). These complex interactions between the disease level and capital level1 are examined in a simple discrete-time model. Health investment appears as a key variable synthesizing these interactions. Our objective is to investigate the long-term impact of the disease on economic equilibrium. By modeling the decisions of agents focusing on the different ways in which a disease affects an economy. So we also explore the role of variables and parameters key interactions between the disease and the economic equilibrium of long-term. The rest of the paper will be organized as follows: in Section 2, the model and the agent's behavior will be explored, then, in Section 3, the equilibrium and the dynamics of the economy will be assessed. In Section 4, our theoretical results by numerical examples and simulations will be presented. This will, finally, bring us to the conclusion of our paper in Section 5.

We care about health not only because it affects mortality, quality of life and morbidity, but also because it may affect the economic growth. This paper makes the case that poor health due to infectious diseases has effects in explaining some economic downturns. More precisely, we present a closed-economy model with overlapping-generations. We use the general equilibrium model of economic growth to study the incidence of infectious diseases. Using this model, we show that impact of infectious diseases depend on economic incentives, rational and preventive behavior. We considered the agent's preventive behavior explicitly by studying the dynamical system of this economy. Incorporating rational behavior (i.e. individual health investment) in a macroeconomic disease structure is our key theoretical innovation. Our main results are twofold. First, for a given level of capital, the disease function is characterized by a critical threshold. It may be observed that if the disease level of a country is below the critical, then the disease progressively disappears. If, however, it rises above the critical, then the increasing speed of the disease becomes a serious risk factor for the economy, and the state of the economy becomes extremely precarious. Second, when the prevalence of the disease intensifies, it can be observed that the trajectories of the system, representing the economy, diverge towards the long-term equilibrium. The disease tends to disappear due to the relatively low initial degree of prevalence of the disease. However, in the neighborhood of the steady state where the disease level is relatively high, the trajectories of the system gradually move away from equilibrium due to the increasing the spread of disease. The trajectories of capital per capita and prevalence of the disease level, then tend to diverge. This strong finding is generated by our hypothesis of the model. An important consequence of these results is the impact of physical capital due to its influence on health investment policies and disease management. The increase in capital per capita in order to fight against disease is not always sufficient. Indeed, depending on the intensity of the disease, the increase in capital may cause an increase or decrease in aggregate health investment. For example, heightened prevalence of disease can actually dissuade an agent from investing in health even if, we assume that the representative agent's investment has potential benefits in disease management. So, rising capital per capita does not prove very effective when the disease is relatively severe: “The steady-state infection level is reduced from 0.31 to 0.19 percent and capital per capita is reduced from 4 to 3.5.”, p.491 (Cuddington et al., 1994). It is vital to take these factors into account when implementing programs and prevention campaigns to halt and reverse disease (HIV/AIDS) in developing countries. The study of comparative statics also demonstrates that long-term equilibrium is characterized by complex relation between disease level and economic growth due to the level of health investment. The macroeconomic equilibrium can be modified by changing the appropriate microeconomic variables. It is, therefore, crucial to point out that increased health investment is not always sufficient to reverse the spread of disease. It is extremely interesting to assess prevention efforts in the healthcare by investigating both the public and private sectors.