Malaria modelling

Basic malaria models

The history of malaria shows that the disease is transmitted for a long time (e.g. Reiter 2000 and 2001). Therefore it is not surprising that malaria models were developed very early. The first pioneer in this field was Ross (Gibson 1998; Ross 1911), who described the malaria transmission by a set of two differential equations.
Basically, the developed malaria models primarily differ in the used method. Initially scientists developed mathematical malaria models, which systematically try to describe the relevant involved biological processes involved. These also called biological or process-based models of malaria transmission are finally arranged in a set of differential or difference equations (e.g. MacDonald 1957; Dietz et al. 1974). A disadvantage of such classic differential-equation malaria models (McKenzie et al. 2001) is the unrealistic assumption of quasi-static vector numbers and unvarying parasite development rates (Hoshen and Morse 2004). For this reason a refinement in modelling techniques was required. At first a seasonal variation in the mosquito numbers was introduced (Anderson and May 1991). The development of climate- or weather-driven malaria models that are using temperature, precipitation or other meteorological data as input variables allowed a better understanding of the dynamic of the malaria transmission. Many involved biological processes involved in the spread of malaria are temperature dependent (e.g. the length of the sporogonic cycle). On the other hand malaria transmission occurs only when rainfall provides temporary breeding habitats for vectors (Hay et al. 2000). In many cases such mathematical malaria models assess the impact of climate change on the global malaria transmission (e.g. Lindsay and Birley 1996; Martens et al. 1995a, 1995b, 1997 and 1999; Lindsay and Martens 1998).

Recent malaria modelling

So far the refinements of those biological models are based on modifications of an equation describing the transmission potential (Rogers and Randolph 2000), since basic knowledge of Anopheles biology is lacking (Depinay et al. 2004). As a resort various malaria models were developed that are based on statistics and that try to avoid the inaccuracy by a more direct approach. Since weekly biting rates in Kenia are stronger correlated with modelled soil moisture than meteorological variables the creation of a statistical hydrological malaria model is principally possible (Patz et al. 1998). In an alternative statistical approach Rogers and Randolph (2000) first establish the current multivariate climatic constraints of the recorded present-day global distribution of malaria. A maximum likelihood method finally enables the prediction of the malaria transmission in future climate scenarios. In a similar statistical regression approach Hay et al. (2002d) find that numbers of months suitable for transmission have not significantly changed during the past century. The implementation of Malaria Early Warning Systems (MEWS) in order to intervene malaria outbreaks is possible by statistical approaches. Hay et al. (2001) and Thompson et al. (2006) exploit a simple quadratic relationship between malaria incidence and precipitation to obtain malaria incidence predictions in epidemic-prone areas.
Due to the increasing computer power more recent versions of malaria models are becoming computationally intensive. McKenzie et al. (1998, 1999, 2001 and 2002) use a discrete-event model that is calculating the transmission status of female mosquitoes and humans. However, the mosquito-dynamics are restricted in terms of "high-season" and "low-season" values when a constant population size is maintained. Depinay et al. (2004) designed a simulation model of African Anopheles ecology and population dynamics that incorporates basic biological requirements for Anopheles development and is using local environmental input data. The model takes various biological and physical aspects into account, e.g. four mosquito stages, a nutrient competition, predation and disease or water body characteristics. However, the knowledge of basic Anopheles biology is often lacking, therefore various assumptions are indispensable. Gu et al. (2003) present a individual based model of malaria transmission that tracks the dynamics of human hosts and adult female mosquitoes individually. However, the model formulation requires observed entomological field data since the seasonal fluctuation of the mosquito population is not simulated. Killeen et al. (2000a) introduce a malaria model based on the life histories of individual mosquitoes and it is driven by input parameters measured in the field. Therefore the application of the last two models is limited to areas where field studies took place.