Epidemics have been studied though modeling of their dynamic. The aim of epidemic modelling is to understand and if possible control the spread of disease. To do this, it tries to relate disease dynamics at the population level to basic properties of the host and pathogen populations and of the infection process [5]
Each year, millions of people worldwide die from infectious diseases such as measles, malaria, tuberculosis, and HIV. While there are many complicating factors, simple mathematical models can provide much insight into the dynamics of disease epidemics and help officials make decisions about public health policy.
The aim of the mathematical modeling of epidemics is to identify those mechanisms that produce such patterns giving a rational description of these events and providing tools for disease control [15].
Modeling allows for estimation of epidemiologic parameters from data, identification of likely mechanisms underlying observed patterns, assessment of the relative merits of alternative control strategies, and prediction of epidemiologic or evolutionary dynamics. The goal of any modeling exercise is to extract as much information as possible from available data and provide an accurate representation of both the knowledge and uncertainty about the epidemic [9].
Modeling aids in decision-making, summarizing and communicating those decisions, monitoring performance and adjusting strategy accordingly, it provides a tool for optimizing investments, and encompasses a rich spectrum of possibilities between 'purely practical' and 'purely academic' approaches. Mathematical models have long been a means of understanding malaria epidemiology and targeting interventions, through simple representation of the underlying biology [16].
The practical use of epidemic models must rely heavily on the realism put into the models. This doesn't mean that a reasonable model can include all possible effects but rather incorporate the mechanisms in the simplest possible fashion so as to maintain major components that influence disease propagation.
Various models have been proposed for modeling epidemics [1-20].
The Kermack-McKendrick model [11] is the first one to provide a mathematical description for kinetic transmission of an epidemic in an unstructured population.
The work in Ref. [11] has had a major influence on the development of mathematical models for disease spread and is still relevant in many epidemic situations. Several extensions of the model have been considered.
On the other front, given the same epidemics say the Malaria for instance, its evolution in Europe does diverge from the evolution in Africa, and in Asia as well. In fact, there is a strong dependence between the climate and the frequency of appearance of the vectors of Malaria (i.e. Mosquitoes).
The study of spatio-temporal distribution of malaria and its
evolution in time and space are of a great importance. Indeed, the development of risk map can guide in establishing programs against this disease. This can benefit from appropriate statistical methods .
Mathematical modelling is increasingly being applied to interpret and predict the dynamics and control of infectious diseases in order to improve global health.
Mathematical models are important tools for decision making in the control of infectious diseases, and malaria was one of the first infections for which such modelling was applied. However, there is still an urgent need for new models that can compare the potential impact of a comprehensive range of malaria interventions.
2. Modeling of malaria transmission(Germany paper)
Transmission and distribution of vector-borne diseases are greatly influenced by environmental and climatic factors. In case of malaria, the ecology, development, behavior, and survival of mosquitoes and the transmission dynamics of the diseases they transmit are strongly influenced by climatic factors [2,5,6,7,8]. Modeling of malaria transmission should incorporate the influence of climatic factors in the model. Unfortunately, few model have been proposed in that way [8,9].
To improve the results proposed so far in the vast literature on the modeling of malaria , we propose a model which describe the interaction between human and mosquitoes when taking into account the influence of climate.
This is because the rains provide more sites for the mosquito larvae to develop, but there is a delay because this takes time for the mosquitoes to mature and it also takes time from when a human is bitten to when they become infectious (see biology pages). It also takes time for the number of cases to build up to the peak level.
1. it is difficult to get the amount of good quality data which are needed for this type of modelling. For example, quality assured malaria data for more than a few years are very difficult to find for most African countries. The more years of good data there are, the more reliable the model is. But in some countries (especially in Africa) these data sets are often incomplete or non-existent;
Symptoms & signs
The initial symptoms are similar to 'flu like illnesses and can include fevers, aches, sore throat and pains and chills.
Other symptoms may include vomiting and nausea, diarrhea; and can rapidly lead to more serious life threatening effects that can develop without treatment.
The main problem is that the early symptoms can be mistaken for something less serious. Symptoms can occur within seven days of entering a malarious area or up to six months of leaving such an area.
Demographic impacts: infant mortality
As mentioned in the introduction, malaria kills as a minimum between 700,000 and 2,700,000 people per year and there are at least 300 million acute cases of malaria each year globally.
We have seen throughout this section, that the burden of malaria is not evenly distributed across all countries. This is due to a combination of climatic factors and also economic factors (the ability to control the disease). Because of the variation in these factors, 90% of all malaria deaths occur in the poorest countries in Sub-Saharan Africa.
Malaria also doesn't affect every person to the same extent, and children are most likely to be seriously ill, and to die from the disease. Others at risk include pregnant women (susceptibility to malaria increases in women who are otherwise immune to malaria when they are pregnant); adults in non-endemic regions, and visitors to areas with malaria.
According to the WHO, in 2002, malaria was the 4th highest cause of death in children under 5 years old, causing 10.7% of deaths. In comparison, HIV/AIDS only caused 3.6% of deaths in this age range.
The combination of climatic, economic, and age-related factors mean that whilst malaria is the leading cause of death annually, most people who die from malaria are African children, less than 5 years old.
In fact, the WHO estimates that at least 20% of all children under the age of 5 who die in Africa, die of malaria.
Social impacts: morbidity
Whilst these deaths have obviously devastating affects for the family and friends of those who die, there are other social and demographic impacts of malaria.
The first of these is the causing of long term disability. As mentioned previously in this section, there are various different types of malaria, the most serious being malaria which affects the brain: this is called cerebral malaria. This is the most deadly of all the strains of malaria, but if it doesn't cause death, it can still have serious implications in terms of causing disability.
The WHO estimate that 2% of children who recover from cerebral malaria will suffer long term learning impairments. This will mean that there is an extra burden on their families to care for them, and that their ability to contribute economically to the household will be impaired. As we will see later on this page, because malaria is most common in economically poor countries, this loss of wage earning potential can be devastating.
Economic impacts: impacts of poverty on malaria
There is a clear correlation between countries affected by malaria, and those which have high levels of poverty. The reason for this correlation could be seen in two ways - it is a bit of a 'which came first, the chicken or the egg?' question.
Obviously, climatic factors play a major part in determining the presence of malaria in a country, and so high levels of poverty alone cannot cause cases of malaria. However, some countries with high incomes have climatic conditions which are right for malaria transmission, but no malaria (such as parts of the USA). This is because richer countries such as the USA can afford the resources needed to control malaria transmission and so the impact of the disease is minimal.
In contrast, countries (such as those in Africa) which can't afford the mass public health strategies needed to control malaria transmission are affected greatly by malaria. The graph on the left shows the percentage of children sleeping under insecticide treated bednets in various African countries. CLick to see bigger version.
So, in this way, we can see that whilst poverty doesn't cause malaria, it does mean that the impact of the disease is much worse.
Economic impacts: impacts of malaria on poverty
But, malaria can also worsen poverty problems. For example, it has been estimated by the WHO that economic growth is 1.3% lower per year in countries affected by malaria. This doesn't sound very much, but over 15 years, this would mean a 20% difference in economic growth. This means that those countries with malaria have much less potential to develop economically.
So why does malaria have such an affect on economic growth? Malaria has economic impacts both directly and indirectly.
Direct costs are things such as the costs of providing health care for those who are infected, the costs of funerals for those who die, and the costs of public health measures such as spraying with insecticides to try to control the spread of the disease.
Indirect costs include the loss of productivity due to illness (people may have to take time off work), and the loss of the potential future earnings of those who are killed or suffer long term disability as a result of malaria.
These costs can be high, for example, it is estimated that in 1997-1998 in South Africa, Malaria cost US$20 million.
In countries where there is little money available for public spending, the burden of these costs constitutes a large proportion of the money available. The WHO estimates that in some countries where the burden of malaria is high, malaria accounts for:
Economic impacts: malaria and poverty at a national scale
But it is not just internationally that the links between malaria and poverty are felt, there are also variations within countries. Rural areas are most affected as it is more difficult to get access to health care, and labour intensive industries such as agriculture are the main employers, and so any loss of life, or loss of productivity due to illness, will have a great impact on the local economy.
In addition to these regional differences, malaria also affects the poorest section of society the most. This is because medical care and prevention may be expensive, and low cost housing is less likely to provide protection against mosquitoes.
For example, a study carried out in Tanzania found that deaths of children under 5 following a high fever (often an indication of malaria) were 39% higher in the poorest socio-economic group than they were in the richest.
As well as being affected more, the cost of treatment, prevention and the indirect costs due to malaria are higher as a proportion of the total money available for poorer households. A study in Ghana showed that whilst the cost of malaria was only 1% of the income of the richest households, it was 34% of the income of the poorest households.
From this, it is easy to see that there are strong links between malaria and poverty. Malaria can contribute to poverty, and poverty can also make the impacts of malaria much worse, so it is a vicious circle. This means that malaria has great impacts on past, present and future economic development for developing countries.
When the burden of malaria is combined with other diseases which have greater impacts on less economically developed countries, such as TB and HIV/AIDS, it is clear that epidemic disease control and development issues are closely related and need to be dealt with in a joined up way.
