Modelling the Transmission of Coxiella burnetii within a UK Dairy Herd: Investigating the Interconnected Relationship between the Parturition Cycle and Environment Contamination
Abstract
:Simple Summary
Abstract
1. Introduction
2. Material and Methods
2.1. The C. burnetii within-Herd Transmission Model
2.1.1. The Infection Cycle
2.1.2. Farm Demographics
2.1.3. Contamination of the Environment
2.2. The Mathematical Formulation of the Model
2.2.1. Model Parameterization and Parameter Reduction
2.3. Initial Conditions
2.4. Sensitivity Analysis
3. Results
3.1. The Standard Case
3.1.1. The Effect of Farm Demographics on the Infection Cycle
3.1.2. The Heterogeneity of the Environmental Contamination
3.2. Sensitivity Analysis
- , that is, the reduction rate of transmission probability by the indoors environment, which essentially provides a measure of the uniformity of the transmission rate in the different environmental compartments: the higher the value of the more uniform the distribution of the transmission rates. There are currently no field or experimental data available in the literature for this parameter, therefore its uncertainty in the current study is high. Previous studies have not considered compartmentalisation of the environment, thus it is a new result highlighted by our model. Consequently, future experimental or field studies should focus on estimating this parameter. It is noted that the of is positive/negative for the seropositive/seronegative prevalence, suggesting that the more uniform the transmission rates become among the different environmental compartments, the more the seropositive sub-population.
- and , expressing the rates from to and vice versa, i.e., asymptomatic to infected. In the current study, data available from the literature were used to calibrate these parameters [7,12,23]; yet all the previous studies were performed in French cattle herds and did not distinguish between exposed and asymptomatic cattle. Therefore, there is some need for further research to enable a potentially more accurate description of these parameters.
- , that is the ratio of reduced transmission from nulliparous cattle. There is no data available in the literature for this parameter, hence, it is characterised by high uncertainty. As a result, further research is required to this regard. The importance of this parameter is also underlined by the fact that previous studies conclude that vaccination should be focused on nulliparous cattle [7,34,35];
3.3. The Effect of the Outdoors Environment on the Infection Cycle
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Parameterization of the Model
Appendix A.1. Transmission Related Parameters
Appendix A.2. Infection Cycle Related Parameters
Appendix A.3. Farm Demography Related Parameters
Appendix A.4. Environmental Contamination Related Parameters
Appendix B. The Equilibria of the Q Fever Model
Appendix C. Confidence Level of the Model’s Response
References
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Parameter | Unit | Description | Source | |
---|---|---|---|---|
, | - | Proportion of time per year for which cattle stay indoors and outdoors | Equation (6) | |
, | day−1 | Transmission rates of becoming from each indoor and outdoor contaminated landscape | Equation (7) | |
, | - | Reduction rate of transmission probability by indoor and outdoor environment | Assumed | |
day−1 | Total indoor transmission rate | [12,17] | ||
day−1 | Total outdoor transmission rate | CtM [12,26,27] | ||
- | Ratio of reduced transmission rate for nulliparous cattle | Assumed | ||
day−1 | Transition rate of eliminating the disease | [7,12] | ||
day−1 | Transition rate of becoming | [21] | ||
day−1 | Transition rate of becoming | CtM [7,12,23] | ||
day−1 | Transition rate of becoming | [7,12] | ||
c | day−1 | Removal rate of due to culling and isolation | [7] | |
day−1 | Progression rate from nulliparous to multiparous cattle | CtM [28] | ||
b | day−1 | Birth rate of multiparous cattle | [7,29,30,31] | |
- | Probability of the offspring being exposed after birth from | [7,32] | ||
b | day−1 | Natural death and removal rate | CtM [7,12,17] | |
day−1 | Indoor shedding rate from | [7,12,17] | ||
- | Indoor birth shedding rate from | CtM [16] | ||
day−1 | Outdoor shedding rate from | Assumed | ||
day−1 | Natural indoor environment decay rate | CtM [17] | ||
day−1 | Natural outdoor environment decay rate | Assumed | ||
day−1 | Active clearing rate of contaminated indoor environment | [17] |
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Patsatzis, D.G.; Wheelhouse, N.; Tingas, E.-A. Modelling the Transmission of Coxiella burnetii within a UK Dairy Herd: Investigating the Interconnected Relationship between the Parturition Cycle and Environment Contamination. Vet. Sci. 2022, 9, 522. https://doi.org/10.3390/vetsci9100522
Patsatzis DG, Wheelhouse N, Tingas E-A. Modelling the Transmission of Coxiella burnetii within a UK Dairy Herd: Investigating the Interconnected Relationship between the Parturition Cycle and Environment Contamination. Veterinary Sciences. 2022; 9(10):522. https://doi.org/10.3390/vetsci9100522
Chicago/Turabian StylePatsatzis, Dimitrios G., Nick Wheelhouse, and Efstathios-Al. Tingas. 2022. "Modelling the Transmission of Coxiella burnetii within a UK Dairy Herd: Investigating the Interconnected Relationship between the Parturition Cycle and Environment Contamination" Veterinary Sciences 9, no. 10: 522. https://doi.org/10.3390/vetsci9100522