Mathematical Model of the Acute Inflammatory Response to Escherichia coli in Intramammary Challenge

Detilleux, Johann; Vangroenweghe, Frédéric; Burvenich, Christian

doi:10.3168/jds.s0022-0302(06)72383-9

Cited by 14 publications

(22 citation statements)

References 60 publications

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“…assuming an SI model ( Anderson and May, 1992;Detilleux et al, 2006). Then, data from genetic and epidemiological studies could be combined to analyze the impact of selecting for a better ability to recover from disease on the spread of the disease at the population level.…”

Section: Resultsmentioning

confidence: 99%

A hidden Markov model to predict early mastitis from test-day somatic cell scores

Detilleux

2011

Animal

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In many countries, high somatic cell scores (SCS) in milk are used as an indicator for mastitis because they are collected on a routine basis. However, individual test-day SCS are not very accurate in identifying infected cows. Mathematical models may improve the accuracy of the biological marker by making better use of the information contained in the available data. Here, a simple hidden Markov model (HMM) is described mathematically and applied to SCS recorded monthly on cows with or without clinical mastitis to evaluate its accuracy in estimating parameters (mean, variance and transition probabilities) under healthy or diseased states. The SCS means were estimated at 1.96 (s.d. 5 0.16) and 4.73 (s.d. 5 0.71) for the hidden healthy and infected states, and the common variance at 0.83 (s.d. 5 0.11). The probability of remaining uninfected, recovering from infection, getting newly infected and remaining infected between consecutive test days was estimated at 78.84%, 60.49%, 11.70% and 15%, respectively. Three different health-related states were compared: clinical stages observed by farmers, subclinical cases defined for somatic cell counts below or above 250 000 cells/ml and infected stages obtained from the HMM. The results showed that HMM identifies infected cows before the appearance of clinical and subclinical signs, which may critically improve the power of the studies on the genetic determinants of SCS and reduce biases in predicting breeding values for SCS.

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Section: Resultsmentioning

confidence: 99%

A hidden Markov model to predict early mastitis from test-day somatic cell scores

Detilleux

2011

Animal

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“…For example, transmission rates have been estimated at 0.20 to 1.50 per 1000 quarter-days at risk for S. uberis mastitis [21] but at 7 to 50 for S. aureus mastitis [22]. Similarly, killing rates have been estimated at 0.67 to 1.33 × 10 -8 mL/cell per min in milk of cows [23,24] and at 1.64 to 1.76 × 10 -8 mL/neutrophil per min in dermis of rats inoculated with E. coli [13]. Model outputs will also depend on the virulence of the invading pathogens (ω), as exemplified by the different amount of milk loss at the first occurrence of clinical mastitis depending on bacteria species [25], and on the type of performance (e.g., yield, quality of products, or capacity for work) considered.…”

Section: Discussionmentioning

confidence: 99%

“…The course of infection within hosts can also be modelled more accurately, in line with the characteristics of the disease under study. For example, models with increasing complexity have been proposed to describe the fate of mastitis-causing E. coli in infected cows [23,24]. Models for co-evolutionary mechanisms between host and pathogens should be considered [38] if the time scale is longer than the one used in this study.…”

Section: Discussionmentioning

confidence: 99%

Effectiveness analysis of resistance and tolerance to infection

Detilleux

2011

Genet Sel Evol

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BackgroundTolerance and resistance provide animals with two distinct strategies to fight infectious pathogens and may exhibit different evolutionary dynamics. However, few studies have investigated these mechanisms in the case of animal diseases under commercial constraints.MethodsThe paper proposes a method to simultaneously describe (1) the dynamics of transmission of a contagious pathogen between animals, (2) the growth and death of the pathogen within infected hosts and (3) the effects on their performances. The effectiveness of increasing individual levels of tolerance and resistance is evaluated by the number of infected animals and the performance at the population level.ResultsThe model is applied to a particular set of parameters and different combinations of values. Given these imputed values, it is shown that higher levels of individual tolerance should be more effective than increased levels of resistance in commercial populations. As a practical example, a method is proposed to measure levels of animal tolerance to bovine mastitis.ConclusionsThe model provides a general framework and some tools to maximize health and performances of a population under infection. Limits and assumptions of the model are clearly identified so it can be improved for different epidemiological settings.

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“…from latent infected to diseased to recovered state in compartmental models for micro-parasitic infections or more explicit descriptions of the life cycle of macro-parasites within and outside the host ( Anderson and May, 1991)), they will not be considered here as they aim to address questions concerning disease prevalence in the population rather than in individual animals. Published models that concentrate on the within-host dynamics of infections exist for nematode infections in ruminants (Louie et al, 2005;Vagenas et al, 2007a and2007b), gut and mammary gland infections in cattle caused by Escherichia coli and other bacterial infections related to mastitis in cattle (Oltenacu and Natzke, 1976;Detilleux, 2004;Detilleux et al, 2006;Wood et al, 2006a and2006b;White et al, 2010) and porcine reproductive and respiratory syndrome (PRRS) in pigs (Doeschl- Wilson and Galina-Pantoja, 2010). …”

Section: Category 1: Models Of Infection and Immune System Dynamicsmentioning

confidence: 99%

“…A more data-driven approach was adopted by Detilleux et al (2006), who modelled the acute inflammatory response to E. coli of the bovine mammary gland. Their deterministic model consists of three relatively simple ordinary differential equations (ODEs) that describe the interactions between bacteria, milk somatic cells and blood leucocyte densities.…”

Section: Prrsv (Virus) Infection (See Example 1)mentioning

confidence: 99%

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

Doeschl‐Wilson

2011

Animal

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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.

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Mathematical Model of the Acute Inflammatory Response to Escherichia coli in Intramammary Challenge

Cited by 14 publications

References 60 publications

A hidden Markov model to predict early mastitis from test-day somatic cell scores

A hidden Markov model to predict early mastitis from test-day somatic cell scores

Effectiveness analysis of resistance and tolerance to infection

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

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