Abstract: Several gastro-intestinal infections in animal husbandry not only greatly reduce the well-being of animals, but also have the potential to cause large economical damage. Understanding of the dynamics of such diseases is thus of great importance. In this paper, we focus on within-host dynamics and present a model describing the dynamics of pathogens in the intestine of a single host. Our motivation to study the problem stems from the case of enterotoxigenic Escherichia coli in newly weaned piglets, but the models we present offer an acceptable description of within-host dynamics of several other gastro-intestinal infections. We begin by studying the case where infection is a one-time event and derive an explicit expression for the distribution of pathogens inside the intestine at an arbitrary time after the infection took place. Since farm animals often come into contact with faeces, we furthermore investigate the reinfection case, in which a fraction of the shed pathogens is reintroduced into the intestine. We find the condition that guarantees persistence of colonization in the reinfection case and determine when the microbial distribution in the intestine obeys the so called asynchronous exponential growth. We outline possibilities for infection control and point out some challenges for further research on the subject.
Abstract: Parasites reproduce and are subject to natural selection at several different, but intertwined, levels. In the recent paper, Gilchrist and Coombs (Theor. Popul. Biol. 69:145â153, 2006) relate the between-host transmission in the context of an SI model to the dynamics within a host. They demonstrate that within-host selection may lead to an outcome that differs from the outcome of selection at the host population level. In this paper we combine the two levels of reproduction by considering the possibility of superinfection and study the evolution of the pathogenâs within-host reproduction rate p. We introduce a superinfection function Ï = Ï(p,q), giving the probability with which pathogens with trait q, upon transmission to a host that is already infected by pathogens with trait p, âtake overâ the host. We consider three cases according to whether the function q â Ï(p,q) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in q = p. We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when Ï is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.
Abstract: Nosocomial bacterial infections in critically ill patients are generally preceded by asymptomatic carriage (i.e. colonization) at one, or even several, body sites such as the skin, the gastro-intestinal and the respiratory tract. Different routes of transmission between the colonized sites create a complex epidemiology, which is additionally complicated by the smallness of the patient population size and the rapid patient turnover, characteristic for intensive care units (ICUs). Naturally occurring large fluctuations in the prevalence of colonization make it very difficult to determine the efficacy of control measures that aim to reduce the prevalence of antibiotic-resistant bacteria in ICUs. Theoretical models can sharpen our intuition through carefully designed thought experiments. In this spirit, we introduce and investigate two models that incorporate the fact that patients may be colonized at multiple body sites. Our study can be applied to several pathogens commonly found in ICUs, such Pseudomonas Aeruginosa, enteric Gram-negative bacteria, MRSA and enterococci. We evaluate the effects of barrier precautions (improved hygiene, use of gloves and gowns, etc.) and of administration of nonabsorbable antibiotics on the prevalence of colonization in ICUs and find that the effect of the controversial, though widely used, antibiotic prophylaxis can only be substantial if the patient-to-patient transmission has already been reduced to a subcritical level by barrier precautions. Taking into account that the very use of antibiotics may increase the selection for resistant strains and may thereby only add to the ever increasing problem of antibiotic resistance, our findings hence represent a firm theoretical argument against the routine use of topical antimicrobial prophylaxis for infection control.
Abstract: In this paper we study deterministic, finite dimensional, continuous as well as discrete time population invasion models. The ability of a newly introduced population, either a new species or a reproductively isolated subpopulation of one of the already present species, to settle in the community relies upon the basic reproduction ratio of the invader, R_0. When R_0 exceeds one the invading
population meets with success and when R_0 is below one the invasion fails. The aim of this paper is to investigate the possible effects of an invasion when the parameters of a model are varied so that R_0 of the invading population passes the value one. We argue that population invasion models, regardless of the biology that underlies them, take a specific form that significantly simplifies the centre manifold analysis. We make a uniform study of ecological, adaptive dynamics and disease
transmission models and derive a simple formula for the direction of bifurcation from a steady state in which only the resident populations are present. We furthermore observe that among those bifurcation parameters that satisfy a certain condition, we acquire the same direction of bifurcation. The obtained mathematical results are used to gain insight into the biology of invasions. The theory is
illustrated by several examples.
