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The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples(More)
Increasing evidence that the strengths of interactions among populations in biological communities form patterns that are crucial for system stability requires clarification of the precise form of these patterns, how they come about, and why they influence stability. We show that in real food webs, interaction strengths are organized in trophic loops in(More)
A ubiquitous quantity in epidemic modelling is the basic reproduction number R(0). This became so popular in the 1990s that 'All you need know is R(0)!' became a familiar catch-phrase. The value of R(0) defines, among other things, the control effort needed to eliminate the infection from a homogeneous host population, but can be misleading when applied to(More)
The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the(More)
We propose a new threshold quantity for the analysis of the epidemiology of infectious diseases. The quantity is similar in concept to the familiar basic reproduction ratio, R0, but it singles out particular host types instead of providing a criterion that is uniform for all host types. Using this methodology we are able to identify the long-term effects of(More)
Habitat fragmentation is generally considered to be detrimental to the persistence of natural populations. In nature management, one therefore tends to prefer few large nature reserves over many small nature reserves having equal total area. This paper examines whether this preference is warranted in a metapopulation framework with circular reserves(More)
In this paper I present the genesis of R0 in demography, ecology and epidemiology, from embryo to its current adult form. I argue on why it has taken so long for the concept to mature in epidemiology when there were ample opportunities for cross-fertilisation from demography and ecology from where it reached adulthood fifty years earlier. Today, R0 is a(More)
Pastoral cattle live in highly structured communities characterized by complex contact patterns. The present paper describes a spatially heterogeneous model for the transmission of contagious bovine pleuropneumonia (CBPP) developed specifically for pastoral communities of East Africa. The model is validated against serological data on the prevalence of CBPP(More)
Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at different life-history stages, or because there are multiple transmission routes. Tick-borne diseases are an important example(More)
Understanding how complex food webs assemble through time is fundamental both for ecological theory and for the development of sustainable strategies of ecosystem conservation and restoration. The build-up of complexity in communities is theoretically difficult, because in random-pattern models complexity leads to instability. There is growing evidence,(More)