F. Ellis McKenzie

Revisiting the Basic Reproductive Number for Malaria and Its Implications for Malaria Control

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.

Statics and dynamics of malaria infection in Anopheles mosquitoes

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 1950s.

The Risk of a Mosquito-Borne Infectionin a Heterogeneous Environment

A common assumption about malaria, dengue, and other mosquito-borne infections is that the two main components of the risk of human infection—the rate at which people are bitten (human biting rate) and the proportion of mosquitoes that are infectious—are positively correlated. In fact, these two risk factors are generated by different processes and may be negatively correlated across space and time in heterogeneous environments. Uneven distribution of blood-meal hosts and larval habitat creates a spatial mosaic of demograPhic sources and sinks. Moreover, mosquito populations fluctuate temporally, forced by environmental variables such as rainfall, temperature, and humidity. These sources of spatial and temporal heterogeneity in the distribution of mosquito populations generate variability in the human biting rate, in the proportion of mosquitoes that are infectious, and in the risk of human infection. To understand how heterogeneity affects the epidemiology of mosquito-borne infections, we developed a set of simple models that incorporate heterogeneity in a stepwise fashion. These models predict that the human biting rate is highest shortly after the mosquito densities peak, near breeding sites where adult mosquitoes emerge, and around the edges of areas where humans are aggregated. In contrast, the proportion of mosquitoes that are infectious reflects the age structure of mosquito populations; it peaks where old mosquitoes are found, far from mosquito breeding habitat, and when mosquito population density is declining. Finally, we show that estimates for the average risk of infection that are based on the average entomological inoculation rate are strongly biased in heterogeneous environments.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Gametocytogenesis : the puberty of Plasmodium falciparum

The protozoan Plasmodium falciparum has a complex life cycle in which asexual multiplication in the vertebrate host alternates with an obligate sexual reproduction in the anopheline mosquito. Apart from the apparent recombination advantages conferred by sex, P. falciparum has evolved a remarkable biology and adaptive phenotypes to insure its transmission despite the dangers of sex. This review mainly focuses on the current knowledge on commitment to sexual development, gametocytogenesis and the evolutionary significance of various aspects of gametocyte biology. It goes further than pure biology to look at the strategies used to improve successful transmission. Although gametocytes are inevitable stages for transmission and provide a potential target to fight malaria, they have received less attention than the pathogenic asexual stages. There is a need for research on gametocytes, which are a fascinating stage, responsible to a large extent for the success of P. falciparum.

A Simulation Model of African Anopheles Ecology and Population Dynamics for the Analysis of Malaria Transmission.

BackgroundMalaria is one of the oldest and deadliest infectious diseases in humans. Many mathematical models of malaria have been developed during the past century, and applied to potential interventions. However, malaria remains uncontrolled and is increasing in many areas, as are vector and parasite resistance to insecticides and drugs.MethodsThis study presents a simulation model of African malaria vectors. This individual-based model incorporates current knowledge of the mechanisms underlying Anopheles population dynamics and their relations to the environment. One of its main strengths is that it is based on both biological and environmental variables.ResultsThe model made it possible to structure existing knowledge, assembled in a comprehensive review of the literature, and also pointed out important aspects of basic Anopheles biology about which knowledge is lacking. One simulation showed several patterns similar to those seen in the field, and made it possible to examine different analyses and hypotheses for these patterns; sensitivity analyses on temperature, moisture, predation and preliminary investigations of nutrient competition were also conducted.ConclusionsAlthough based on some mathematical formulae and parameters, this new tool has been developed in order to be as explicit as possible, transparent in use, close to reality and amenable to direct use by field workers. It allows a better understanding of the mechanisms underlying Anopheles population dynamics in general and also a better understanding of the dynamics in specific local geographic environments. It points out many important areas for new investigations that will be critical to effective, efficient, sustainable interventions.

White Blood Cell Counts and Malaria

White blood cells (WBCs) were counted in 4697 individuals who presented to outpatient malaria clinics in Maesod, Tak Province, Thailand, and Iquitos, Peru, between 28 May and 28 August 1998 and between 17 May and 9 July 1999. At each site and in each year, WBC counts in the Plasmodium falciparum-infected patients were lower than those in the Plasmodium vivax-infected patients, which, in turn, were lower than those in the uninfected patients. In Thailand, one-sixth of the P. falciparum-infected patients had WBC counts of <4000 cells/microL. Leukopenia may confound population studies that estimate parasite densities on the basis of an assumed WBC count of 8000 cells/microL. For instance, in the present study, use of this conventional approach would have overestimated average asexual parasite densities in the P. falciparum-infected patients in Thailand by nearly one-third.

Potential Impact of Intermittent Preventive Treatment (IPT) on Spread of Drug-Resistant Malaria

Background Treatment of asymptomatic individuals, regardless of their malaria infection status, with regularly spaced therapeutic doses of antimalarial drugs has been proposed as a method for reducing malaria morbidity and mortality. This strategy, called intermittent preventive treatment (IPT), is currently employed for pregnant women and is being studied for infants (IPTi) as well. As with any drug-based intervention strategy, it is important to understand how implementation may affect the spread of drug-resistant parasites. This is a difficult issue to address experimentally because of the limited size and duration of IPTi trials as well as the intractability of distinguishing the spread of resistance due to conventional treatment of malaria episodes versus that due to IPTi when the same drug is used in both contexts. Methods and Findings Using a mathematical model, we evaluated the possible impact of treating individuals with antimalarial drugs at regular intervals regardless of their infection status. We translated individual treatment strategies and drug pharmacokinetics into parasite population dynamic effects and show that immunity, treatment rate, drug decay kinetics, and presumptive treatment rate are important factors in the spread of drug-resistant parasites. Our model predicts that partially resistant parasites are more likely to spread in low-transmission areas, but fully resistant parasites are more likely to spread under conditions of high transmission, which is consistent with some epidemiological observations. We were also able to distinguish between spread of resistance due to treatment of symptomatic infections and that due to IPTi. We showed that IPTi could accelerate the spread of resistant parasites, but this effect was only likely to be significant in areas of low or unstable transmission. Conclusions The results presented here demonstrate the importance of considering both the half-life of a drug and the existing level of resistance when choosing a drug for IPTi. Drugs to which little or no resistance exists are not advisable for IPT in high-transmission areas, but IPTi is not likely to significantly impact the spread of highly resistant parasites in areas where partial resistance is already established. IPTi is more likely to accelerate the spread of resistance in high-transmission areas than is IPT in adults (i.e., pregnant women).

Environmental factors associated with the malaria vectors Anopheles gambiae and Anopheles funestus in Kenya

BackgroundThe Anopheles gambiae and Anopheles funestus mosquito species complexes are the primary vectors of Plasmodium falciparum malaria in sub-Saharan Africa. To better understand the environmental factors influencing these species, the abundance, distribution and transmission data from a south-eastern Kenyan study were retrospectively analysed, and the climate, vegetation and elevation data in key locations compared.MethodsThirty villages in Malindi, Kilifi and Kwale Districts with data on An. gambiae sensu strict, Anopheles arabiensis and An. funestus entomological inoculation rates (EIRs), were used as focal points for spatial and environmental analyses. Transmission patterns were examined for spatial autocorrelation using the Morans I statistic, and for the clustering of high or low EIR values using the Getis-Ord Gi* statistic. Environmental data were derived from remote-sensed satellite sources of precipitation, temperature, specific humidity, Normalized Difference Vegetation Index (NDVI), and elevation. The relationship between transmission and environmental measures was examined using bivariate correlations, and by comparing environmental means between locations of high and low clustering using the Mann-Whitney U test.ResultsSpatial analyses indicated positive autocorrelation of An. arabiensis and An. funestus transmission, but not of An. gambiae s.s., which was found to be widespread across the study region. The spatial clustering of high EIR values for An. arabiensis was confined to the lowland areas of Malindi, and for An. funestus to the southern districts of Kilifi and Kwale. Overall, An. gambiae s.s. and An. arabiensis had similar spatial and environmental trends, with higher transmission associated with higher precipitation, but lower temperature, humidity and NDVI measures than those locations with lower transmission by these species and/or in locations where transmission by An. funestus was high. Statistical comparisons indicated that precipitation and temperatures were significantly different between the An. arabiensis and An. funestus high and low transmission locations.ConclusionThese finding suggest that the abundance, distribution and malaria transmission of different malaria vectors are driven by different environmental factors. A better understanding of the specific ecological parameters of each malaria mosquito species will help define their current distributions, and how they may currently and prospectively be affected by climate change, interventions and other factors.

Influenza Forecasting in Human Populations: A Scoping Review

Forecasts of influenza activity in human populations could help guide key preparedness tasks. We conducted a scoping review to characterize these methodological approaches and identify research gaps. Adapting the PRISMA methodology for systematic reviews, we searched PubMed, CINAHL, Project Euclid, and Cochrane Database of Systematic Reviews for publications in English since January 1, 2000 using the terms “influenza AND (forecast* OR predict*)”, excluding studies that did not validate forecasts against independent data or incorporate influenza-related surveillance data from the season or pandemic for which the forecasts were applied. We included 35 publications describing population-based (N = 27), medical facility-based (N = 4), and regional or global pandemic spread (N = 4) forecasts. They included areas of North America (N = 15), Europe (N = 14), and/or Asia-Pacific region (N = 4), or had global scope (N = 3). Forecasting models were statistical (N = 18) or epidemiological (N = 17). Five studies used data assimilation methods to update forecasts with new surveillance data. Models used virological (N = 14), syndromic (N = 13), meteorological (N = 6), internet search query (N = 4), and/or other surveillance data as inputs. Forecasting outcomes and validation metrics varied widely. Two studies compared distinct modeling approaches using common data, 2 assessed model calibration, and 1 systematically incorporated expert input. Of the 17 studies using epidemiological models, 8 included sensitivity analysis. This review suggests need for use of good practices in influenza forecasting (e.g., sensitivity analysis); direct comparisons of diverse approaches; assessment of model calibration; integration of subjective expert input; operational research in pilot, real-world applications; and improved mutual understanding among modelers and public health officials.