Statics and Dynamics of Malaria Transmission: The Relationship between Prevalence in Humans and Mosquitoes.

The present paper explores a simple dynamic model from which we review the classic formulae in malaria epidemiology that relate entomological parameters to malaria transmission. In addition, we document the dynamics of malaria, illustrating the impact of control strategies and how the bites per mosquito have a larger effect on transmission intensity than the mosquito mortality, the ratio of mosquitoes to humans, or the transmission efficiency. The model has been built following the System Dynamics methodology, explicitly representing the variables, the feedbacks and the nonlinearities, i.e. the structure that governs the dynamics of the disease. In this sense, the paper offers a new way to obtain the most representative malaria indicators derived from stock-and-flow diagrams that encompass the causal relationships that exist between the attributes of such a system. Based on the obtained formulae from the human and mosquito sectors, we are able to eliminate three degrees of freedom, allowing us to calculate the temporal steady state relationship between Plasmodium falciparum prevalence in humans and mosquitoes. The model is generic in nature and may be parameterized to portray a wide variety of locations, different malaria parasites, vector species, and to cater for seasonality. Given that the model includes the principle mechanisms of malaria transmission, it acts as a foundation for simulations that represent the dynamics between humans and mosquitoes. Such model has been developed based on a number of simplifying assumptions. To the extent possible, the validity of the model under these assumptions has been analyzed by way of mathematic equations.