Abstract
The prospects for the success of malaria control depend, in part, on the basic reproductive number for malaria, R 0. Here, we estimate R 0 in a novel way for 121 African populations, and thereby increase the number of R 0 estimates for malaria by an order of magnitude. The estimates range from around one to more than 3,000. We also consider malaria transmission and control in finite human populations, of size H. We show that classic formulas approximate the expected number of mosquitoes that could trace infection back to one mosquito after one parasite generation, Z 0(H), but they overestimate the expected number of infected humans per infected human, R 0(H). Heterogeneous biting increases R 0 and, as we show, Z 0(H), but we also show that it sometimes reduces R 0(H); those who are bitten most both infect many vectors and absorb infectious bites. The large range of R 0 estimates strongly supports the long-held notion that malaria control presents variable challenges across its transmission spectrum. In populations where R 0 is highest, malaria control will require multiple, integrated methods that target those who are bitten most. Therefore, strategic planning for malaria control should consider R 0, the spatial scale of transmission, human population density, and heterogeneous biting.
Highlights
Each year, Plasmodium falciparum causes approximately 515 million clinical malaria cases [1] and over one million deaths [2,3]
Estimating R0 Our estimates of R0 are based on two more commonly measured indices called the entomological inoculation rate (EIR) (E in equations), which is the average number of infectious bites received by a person in a year, and the parasite rate (PR) (X in equations), which is the prevalence of malaria infection in humans
Indices and parameters; these are the EIR, the PR, the vectorial capacity, V, which measures the number of infectious bites that arise from all the mosquitoes that are infected by a single infectious person on a single day [24], the infectivity of humans to mosquitoes, c, and the stability index, S, which measures the number of human bites taken by a vector during its lifetime [25]
Summary
Plasmodium falciparum causes approximately 515 million clinical malaria cases [1] and over one million deaths [2,3]. Most malaria-related mortality and a large fraction of malaria cases occur in sub-Saharan Africa, where transmission can be very intense [4]. The intensity of malaria transmission affects most aspects of malaria epidemiology and control, including the age at first infection, the fraction of a population that is infected (i.e., the parasite rate [PR]), the frequency and type of disease syndromes, the incidence of severe disease, the development and loss of functional immunity (i.e., immunity that reduces the frequency and severity of clinical symptoms), total malaria mortality, and the expected outcome of malaria control [4,5,6,7,8]. The basic reproductive number, R0, has played a central role in epidemiological theory for malaria and other infectious diseases because it provides an index of transmission intensity and establishes threshold criteria. The fraction of a population that would need to be protected to confer ‘‘herd immunity’’ and interrupt transmission is 1 À 1/R0
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