The role of mathematical models of host–pathogen interactions for livestock health and production – a review

Abstract

Compared with the application of mathematical models to study human diseases, models that describe animal responses to pathogen challenges are relatively rare. The aim of this review is to explain and show the role of mathematical host-pathogen interaction models in providing underpinning knowledge for improving animal health and sustaining livestock production. Existing host-pathogen interaction models can be assigned to one of three categories: (i) models of the infection and immune system dynamics, (ii) models that describe the impact of pathogen challenge on health, survival and production and (iii) models that consider the co-evolution of host and pathogen. State-of-the-art approaches are presented and discussed for models belonging to the first two categories only, as they concentrate on the host-pathogen dynamics within individuals. Models of the third category fall more into the class of epidemiological models, which deserve a review by themselves. An extensive review of published models reveals a rich spectrum of methodologies and approaches adopted in different modelling studies, and a strong discrepancy between models concerning diseases in animals and models aimed at tackling diseases in humans (most of which belong to the first category), with the latter being generally more sophisticated. The importance of accounting for the impact of infection not only on health but also on production poses a considerable challenge to the study of host-pathogen interactions in livestock. This has led to relatively simplistic representations of host-pathogen interaction in existing models for livestock diseases. Although these have proven appropriate for investigating hypotheses concerning the relationships between health and production traits, they do not provide predictions of an animal's response to pathogen challenge of sufficient accuracy that would be required for the design of appropriate disease control strategies. A synthesis between the modelling methodologies adopted in categories 1 and 2 would therefore be desirable. The progress achieved in mathematical modelling to study immunological processes relevant to human diseases, together with the current advances in the generation and analysis of biological data related to animal diseases, offers a great opportunity to develop a new generation of host-pathogen interaction models that take on a fundamental role in the study and control of disease in livestock.

Novel methods for quantifying individual host response to infectious pathogens for genetic analyses

“…There are, however, several challenges associated with the dynamical systems approach, of which perhaps the biggest one is to identify an appropriate model that reproduces the essential features observed from the data. There is a vast literature on dynamic host–pathogen interaction models [see e.g., reviews by Louzoun (2007); Mata and Cohn (2007); Doeschl-Wilson (2011)], ranging from simple models such as the one presented here [Equation (7)], where pathogens and immune response are summarized as single entities (e.g., Antia et al, 1996; Restif and Koella, 2004; Doeschl-Wilson et al, 2009), to highly complex models comprising a large number of differential equations with many parameters (e.g., Marchuck et al, 1991; Kosmrlj et al, 2010). For the purpose of quantitative genetic analyses, simple models requiring fewer parameters and thus giving rise to fewer phenotypic traits are more attractive than complex models.…”

Trends in mathematical modeling of host–pathogen interactions

“…However, CA are gridbased and do not allow a free movement in space as the (usually) lattice-free ABM does [14,21,96,118]. Thus, ABM can be considered as an extension or generalization of CA [26,96]. In the unconventional ABM approach, individual independent agents are defined (such as fungal, bacterial, or human cells) with interaction rules [7,13,21,44,96,118].…”

“…These bottom-up approaches are usually easier to implement than top-down approaches, because it is more comprehensible to describe the behavior of each individual agent than that of the whole system. Also, it can be adapted more flexibly to changing conditions and stochastic factors can easily be included in the rules [7,13,26,96,118]. A further advantage is that the results can be visualized nicely, for example, in colorful videos.…”

“…For example, the interplay of alleles can often be described both by population genetics and game theory [60]. It depends on the aim of study which method is most suitable [26] or may be, to some extent, a matter of taste. This will be discussed in more detail in the section "Conclusion and outlook".…”

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

“…The development of mathematical models in animal science has contributed to gaining insight in different central aspects of animal physiology such as metabolism and digestion. The potential of modelling has been discussed by different authors (France, 1988;Baldwin, 2000;Doeschl-Wilson, 2011).…”