A mathematical model of detection and dynamics of porcine transmissible gastroenteritis

Modelling infectious viral diseases in swine populations: a state of the art

Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.

A discrete-time epidemiological model to quantify selection for disease resistance

A genetic epidemiological model (GEM) for investigating the effect of selection for disease resistance on the epidemiology of infectious diseases is presented and applied to a pig breeding scenario. Fundamental to the model is R0, the basic reproductive ratio. R0 is the expected number of secondary infections caused by a single infection. If R0 is greater than 1, there will be an epidemic. The aim of the model is to quantify the effect of selection on R0 and the consequences this has on disease epidemiology. Two implementations are presented: selection for reduced susceptibility/infectivity to a disease and introgression of a major resistance gene. The results suggest that the effects of selection for reduced susceptibility I infectivity are critically dependent on the infectiousness of the disease. Under the assumptions made in the model, for a disease with a low infection level, it takes approximately 15 years of selection until R0 is less than 1 and the population is safe from epidemics should the infectious agent be present. For a highly infectious disease, this time may be as long as 100 years. For gene introgression, the population is expected to be free from epidemics within 5 years and the time to reduce R0 to less than 1 is largely independent of the disease being considered. With gene introgression, the proportion of the population which needs to be resistant to ensure that R0 is less than one is shown to be a function of the initial R0 for the disease. Although selection, as modelled, results in a linear decline in R0, the reduction in the proportion of animals infected during an epidemic is non-linear. The selection process reduces the amount of infectious material that is in the environment when an infection occurs and this decreases the force of infection on unselected animals. This phenomenon results in a marked interaction between host genotype and disease epidemiology. Thus, the results of the model show that altering the genetics of individual animals affects the epidemiology of the disease at the population level. The model can be applied to any farm structure and any microparasitic infectious disease.

Modelling the within-herd transmission of Mycoplasma hyopneumoniae in closed pig herds

Background

A discrete time, stochastic, compartmental model simulating the spread of Mycoplasma hyopneumoniae within a batch of industrially raised pigs was developed to understand infection dynamics and to assess the impact of a range of husbandry practices. A ‘disease severity’ index was calculated based on the ratio between the cumulative numbers of acutely and chronically diseased and infectious pigs per day in each age category, divided by the length of time that pigs spent in this age category. This is equal to the number of pigs per day, either acutely or chronically infectious and diseased, divided by the number of all pigs per all days in the model. The impact of risk and protective factors at batch level was examined by adjusting ‘acclimatisation of gilts’, ‘length of suckling period’, ‘vaccination of suckling pigs against M. hyopneumoniae’, ‘contact between fattening pigs of different age during restocking of compartments’ and ‘co-infections in fattening pigs’.

Results

The highest ‘disease severity’ was predicted, when gilts do not have contact with live animals during their acclimatisation, suckling period is 28 days, no vaccine is applied, fatteners have contact with pigs of other ages and are suffering from co-infections. Pigs in this scenario become diseased/infectious for 26.1 % of their lifetime. Logistic regression showed that vaccination of suckling pigs was influential for ‘disease severity’ in growers and finishers, but not in suckling and nursery pigs. Lack of contact between gilts and other live pigs during the acclimatisation significantly influenced the ‘disease severity’ in suckling pigs but had less impact in growing and finishing pigs. The length of the suckling period equally affected the severity of the disease in all age groups with the strongest association in nursery pigs. The contact between fatteners of different groups influenced the course of infection among finishers, but not among other pigs. Finally, presence of co-infections was relevant in growers and finishers, but not in younger pigs.

Conclusion

The developed model allows comparison of different prevention programmes and strategies for controlling transmission of M. hyopneumoniae.

Electronic supplementary material

The online version of this article (doi:10.1186/s40813-016-0026-1) contains supplementary material, which is available to authorized users.

Identifying critical parameters in the dynamics and control of microparasite infection using a stochastic epidemiological model

A stochastic epidemic model is presented to study infection transmission dynamics, and hence epidemic severity and disease incidence, in a closed population. The aim was to understand the relative importance of various parameters that influence the dynamics of potential epidemics, particularly when the genetic mechanisms of resistance or tolerance to infection are considered. Simulations explored the effect of varying the transmission coefficient, latent period, recovery period, mortality rate, and the period of loss of immunity on overall epidemic outcomes. The critical parameters influencing the transmission of infection, and hence disease incidence, were the transmission coefficient, the latent period, and the recovery period; the period of loss of immunity had only trivial effects. Ideally, control strategies should decrease the transmission coefficient and/or increase the latent period and/or decrease the recovery period. By equating measured traits with disease transmission parameters, the model described in this paper can be used to identify which disease resistance genes or QTL will be truly effective in helping to develop disease-resistant livestock that suffer fewer epidemics and side-effects of infection. In particular, emphases should be placed on finding genes that decrease the transmission of infection, increase the latent period, or decrease the recovery period.