If the host population is taken to be a dynamic variable (rather than constant, as conventionally assumed), a wider understanding of the population biology of infectious diseases emerges. In this first part of a two-part article, mathematical models are developed, shown to fit data from laboratory experiments, and used to explore the evolutionary relations among transmission parameters. In the second part of the article, to be published in next week's issue, the models are extended to include indirectly transmitted infections, and the general implications for infectious diseases are considered.

Population biology of infectious diseases: Part II

Theory and observation indicate that natural multi-species assemblies of plants and animals are likely to possess several different equilibrium points. This review discusses how alternate stable states can arise in simple 1- and 2-species systems, and applies these ideas to grazing systems, to insect pests, and to some human host–parasite systems.

Thresholds and breakpoints in ecosystems with a multiplicity of stable states

Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the best-studied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples from human and wildlife disease systems to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers. Empirical evidence points to several biologically distinct mechanisms by which seasonality can impact host-pathogen interactions, including seasonal changes in host social behaviour and contact rates, variation in encounters with infective stages in the environment, annual pulses of host births and deaths and changes in host immune defences. Mathematical models and field observations show that the strength and mechanisms of seasonality can alter the spread and persistence of infectious diseases, and that population-level responses can range from simple annual cycles to more complex multiyear fluctuations. From an applied perspective, understanding the timing and causes of seasonality offers important insights into how parasite-host systems operate, how and when parasite control measures should be applied, and how disease risks will respond to anthropogenic climate change and altered patterns of seasonality. Finally, by focusing on well-studied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.

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Seasonality and the dynamics of infectious diseases.

The transmission of infectious diseases is an inherently ecological process involving interactions among at least two, and often many, species. Not surprisingly, then, the species diversity of ecological communities can potentially affect the prevalence of infectious diseases. Although a number of studies have now identified effects of diversity on disease prevalence, the mechanisms underlying these effects remain unclear in many cases. Starting with simple epidemiological models, we describe a suite of mechanisms through which diversity could increase or decrease disease risk, and illustrate the potential applicability of these mechanisms for both vector-borne and non-vector-borne diseases, and for both specialist and generalist pathogens. We review examples of how these mechanisms may operate in specific disease systems. Because the effects of diversity on multi-host disease systems have been the subject of much recent research and controversy, we describe several recent efforts to delineate under what general conditions host diversity should increase or decrease disease prevalence, and illustrate these with examples. Both models and literature reviews suggest that high host diversity is more likely to decrease than increase disease risk. Reduced disease risk with increasing host diversity is especially likely when pathogen transmission is frequency-dependent, and when pathogen transmission is greater within species than between species, particularly when the most competent hosts are also relatively abundant and widespread. We conclude by identifying focal areas for future research, including (1) describing patterns of change in disease risk with changing diversity; (2) identifying the mechanisms responsible for observed changes in risk; (3) clarifying additional mechanisms in a wider range of epidemiological models; and (4) experimentally manipulating disease systems to assess the impact of proposed mechanisms.

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Effects of species diversity on disease risk.

Transmission intensity affects almost all aspects of malaria epidemiology and the impact of malaria on human populations. Maps of transmission intensity are necessary to identify populations at different levels of risk and to evaluate objectively options for disease control. To remain relevant operationally, such maps must be updated frequently. Following the first global effort to map Plasmodium falciparum malaria endemicity in 2007, this paper describes the generation of a new world map for the year 2010. This analysis is extended to provide the first global estimates of two other metrics of transmission intensity for P. falciparum that underpin contemporary questions in malaria control: the entomological inoculation rate (Pf EIR) and the basic reproductive number (PfR). Annual parasite incidence data for 13,449 administrative units in 43 endemic countries were sourced to define the spatial limits of P. falciparum transmission in 2010 and 22,212 P. falciparum parasite rate (Pf PR) surveys were used in a model-based geostatistical (MBG) prediction to create a continuous contemporary surface of malaria endemicity within these limits. A suite of transmission models were developed that link Pf PR to Pf EIR and PfR and these were fitted to field data. These models were combined with the Pf PR map to create new global predictions of Pf EIR and PfR. All output maps included measured uncertainty. An estimated 1.13 and 1.44 billion people worldwide were at risk of unstable and stable P. falciparum malaria, respectively. The majority of the endemic world was predicted with a median Pf EIR of less than one and a median PfRc of less than two. Values of either metric exceeding 10 were almost exclusive to Africa. The uncertainty described in both Pf EIR and PfR was substantial in regions of intense transmission. The year 2010 has a particular significance as an evaluation milestone for malaria global health policy. The maps presented here contribute to a rational basis for control and elimination decisions and can serve as a baseline assessment as the global health community looks ahead to the next series of milestones targeted at 2015.

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A world malaria map: Plasmodium falciparum endemicity in 2007

The Epidemiology and Control of Malaria.

The dynamics of helminth infections, with special reference to schistosomes

The analysis of equilibrium in malaria.

The epidemiology of malaria is discussed with special reference to the pattern observed in equatorial Africa, where the disease is very stable and where certain features, such as severe epidemic tendencies and ready amenability to control, commonly found in other malarious regions, are lacking. The particular conditions giving rise to stability are described in detail, and the ways in which they can be modified to bring about control of the disease in its stable form are outlined. The importance of measuring certain rates-for example, the basic reproduction rate, the index of stability, and the actual reproduction rate-when making any major malaria survey is emphasized, and formulae by means of which such rates can be readily calculated are included in an annex.

George Macdonald

Papers

The Epidemiology and Control of Malaria.

The dynamics of helminth infections, with special reference to schistosomes

The analysis of equilibrium in malaria.

Epidemiological basis of malaria control.

The analysis of the sporozoite rate.