Abstract
The classic formulae in malaria epidemiology are reviewed that relate entomological parameters to malaria transmission, including mosquito survivorship and age-at-infection, the stability index (S), the human blood index (HBI), proportion of infected mosquitoes, the sporozoite rate, the entomological inoculation rate (EIR), vectorial capacity (C) and the basic reproductive number (R0). The synthesis emphasizes the relationships among classic formulae and reformulates a simple dynamic model for the proportion of infected humans. The classic formulae are related to formulae from cyclical feeding models, and some inconsistencies are noted. The classic formulae are used to to illustrate how malaria control reduces malaria transmission and show that increased mosquito mortality has an effect even larger than was proposed by Macdonald in the 1950's.
Highlights
In this paper, the classic formulae in malaria are reviewed and re-derived including explicit and simple formulae for the statics of Plasmodium infection in mosquitoes such as mosquito survivorship, the human blood index (HBI), the stability index (S), the proportion of mosquitoes that are infected, and the proportion of mosquitoes that are infectious
Statics of mosquito infections As in the models used to derive the classic formulae in malaria epidemiology, the following derivations assume that mosquito populations are homogeneous, ignore mosquito senescence, and assume that adult mosquito population size is constant
Vectorial capacity is far removed from the costs and benefits of actual control programmes, but the analysis suggests that mortality of adult mosquitoes is sensitive to control
Summary
Classic formulae for the entomological inoculation rate, basic reproductive number R0, vectorial capacity, and prevalence of infection in humans (the proportion of humans who are infected, or parasite rate) are usually based on the same simplifying assumptions, whether they are formulated as cyclical feeding models or as dynamical equations. The classic assumptions and corresponding models provide a starting point for quantifying malaria transmission and for relating static and dynamic aspects of malaria infection in humans and mosquitoes. They should be regarded as idealizations, serving a purpose similar to that of the Hardy-Weinberg equations in population genetics. Malaria control may require data to estimate relative reductions in mosquito mortality, emergence, or human biting. In such cases, it is more important to have several consistent estimates of epidemiological parameters. The answer should depend on the goals of local malaria control
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