Abstract
A mathematical model is proposed that describes the colonization of host tissues by a contagious pathogen and the early nonspecific immune response, the impact of the infection on the performances of the host, and the spread of the infection in the population. The model obeys specific biological characteristics: Susceptible hosts are infected after contact with an infected one. The number of pathogenic units that invade a susceptible host is dependent on the infectious dose provided by the infected host and on the ability of the susceptible host to resist the invasion. After entry in host, pathogenic changes over time are expressed as the difference between the intrinsic logistic growth rate and the Holling type II kill rate provided by the immune response cells. Hosts have different ability to restrict reproduction of the pathogen units. The number of response cells actively recruited to the site of infection depends on the number of the pathogenic units. Response cells are removed after having killed a fixed number of pathogenic units. The effects of the number of pathogenic units on the performances of the host depend upon its levels of tolerance to the deleterious effects of both pathogenic and response cells. Pre-infection costs are associated to tolerance and resistance levels. Estimates of most biological parameters of the model are based on published experimental studies while resistance/tolerance parameters are varied across their allowable ranges. The model reproduces qualitatively realistic outcomes in response to infection: healthy response, recurrent infection, persistent infectious and non-infectious inflammation, and severe immunodeficiency. Evolution across time at the animal and population levels is presented. Effects on animal performances are discussed with respect to changes in resistance/tolerance parameters and selection strategies are suggested.
Highlights
Many conservation and selection programs (e.g., FAO, 2007; Eadgene, 2012) include increasing ability to fight endemic disease as an objective
infected hosts (It) follows by the effects of different levels of In case of persistent infectious response and immune-depression resistance and tolerance on a healthy response
A mathematical model is proposed to quantify the effects of resistance and tolerance on the spread of an infectious disease and on animal performances within a closed population
Summary
Many conservation and selection programs (e.g., FAO, 2007; Eadgene, 2012) include increasing ability to fight endemic disease as an objective. The first challenge to meet this objective is to accurately define and measure disease resistance and tolerance. Resistance traits are broadly defined as host traits that reduce the extent of pathogen infection. They include traits that reduce pathogen transmission at contact and pathogen growth rate once infection has occurred (Kover and Schaal, 2002). Controlled immune response is a major mediator of resistance because of its efficacy in clearing infections (Sears et al, 2011). Resistance is typically measured as the inverse of infection intensity (number of parasites per host or per unit host tissue) and a lower intensity means an animal is more resistant, all else being equal (Råberg et al, 2009; Medzhitov et al, 2012)
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