Multiscale modelling of scrapie epidemiology

Discrete Models in Epidemiology: New Contagion Probability Functions Based on Real Data Behavior

Mathematical modeling is a tool used for understanding diseases dynamics. The discrete-time model is an especial case in modeling that satisfactorily describes the epidemiological dynamics because of the discrete nature of the real data. However, discrete models reduce their descriptive and fitting potential because of assuming a homogeneous population. Thus, in this paper, we proposed contagion probability functions according to two infection paradigms that consider factors associated with transmission dynamics. For example, we introduced probabilities of establishing an infectious interaction, the number of contacts with infectious and the level of connectivity or social distance within populations. Through the probabilities design, we overcame the homogeneity assumption. Also, we evaluated the proposed probabilities through their introduction into discrete-time models for two diseases and different study zones with real data, COVID-19 for Germany and South Korea, and dengue for Colombia. Also, we described the oscillatory dynamics for the last one using the contagion probabilities alongside parameters with a biological sense. Finally, we highlight the implementation of the proposed probabilities would improve the simulation of the public policy effect of control strategies over an infectious disease outbreak.

Moment approximation of infection dynamics in a population of moving hosts

The modelling of contact processes between hosts is of key importance in epidemiology. Current studies have mainly focused on networks with stationary structures, although we know these structures to be dynamic with continuous appearance and disappearance of links over time. In the case of moving individuals, the contact network cannot be established. Individual-based models (IBMs) can simulate the individual behaviours involved in the contact process. However, with very large populations, they can be hard to simulate and study due to the computational costs. We use the moment approximation (MA) method to approximate a stochastic IBM with an aggregated deterministic model. We illustrate the method with an application in animal epidemiology: the spread of the highly pathogenic virus H5N1 of avian influenza in a poultry flock. The MA method is explained in a didactic way so that it can be reused and extended. We compare the simulation results of three models: 1. an IBM, 2. a MA, and 3. a mean-field (MF). The results show a close agreement between the MA model and the IBM. They highlight the importance for the models to capture the displacement behaviours and the contact processes in the study of disease spread. We also illustrate an original way of using different models of the same system to learn more about the system itself, and about the representation we build of it.

The impact of the genotype on the prevalence of classical scrapie at population level

Total number and genotypes of animals in holdings selected for the genotype & cull option in the Compulsory Scrapie Flock Scheme (CSFS) in Great Britain were extracted from the National Scrapie Plan data warehouse. The association between various genotype-related measures and scrapie prevalence infection was tested using zero-inflated negative binomial models with the counts of positive cases as dependent variable, and country, number of flocks in the scheme, flock size, surveillance source and the following genotype-related measurements: the centered-log ratios (clr) oof the 15 genotypes, of the proportions of the 5 alleles at codons 136, 154 and 171, of the proportions of the 5 NSP types, and two flock-susceptibility risk indicators, as explanatory variables. A total of 319341 genotyped animals from 168 holdings were included in the analysis. An increased proportion of the ARR/ARR genotype corresponded to a decrease in the number of scrapie cases. ARR/AHQ, AHQ/VRQ, ARH/VRQ and ARQ/VRQ genotypes, NSP type V, ARH, ARQ, AHQ and VRQ alleles and the low and high-susceptibility risk indicators are all associated with an increase risk in the number of scrapie cases.

Regardless the management practices; the increased susceptibility that the non-ARR alleles confer on an individual could be extrapolated at the population level. Increasing prevalence of ARR allele reduces the overall risk of scrapie at population level. At genotype level, the VRQ/VRQ genotype, present a very low frequency in the study population, seems to play a residual effect in the overall risk of scrapie in a flock.

The role of mathematical modelling in understanding the epidemiology and control of sheep transmissible spongiform encephalopathies: a review

To deal with the incompleteness of observations and disentangle the complexities of transmission much use has been made of mathematical modelling when investigating the epidemiology of sheep transmissible spongiform encephalopathies (TSE) and, in particular, scrapie. Importantly, these modelling approaches allow the incidence of clinical disease to be related to the underlying prevalence of infection, thereby overcoming one of the major difficulties when studying these diseases. Models have been used to investigate the epidemiology of scrapie within individual flocks and at a regional level; to assess the efficacy of different control strategies, especially selective breeding programmes based on prion protein (PrP) genotype; to interpret the results of scrapie surveillance; and to inform the design of surveillance programmes. Furthermore, mathematical modelling has played an important role when assessing the risk to human health posed by the possible presence of bovine spongiform encephalopathy in sheep. Here, we review the various approaches that have been taken when developing and analysing mathematical models for the epidemiology and control of sheep TSE and assess their impact on our understanding of these diseases. We also identify areas that require further work, discuss future challenges and identify data gaps.

PrP genotype: a flock-level risk factor for scrapie?

Previous epidemiological studies of risk factors for classical scrapie at flock level have identified a variety of management and purchase related variables, along with increased flock size and, in some cases, breed effects. Although known as a risk factor at the individual animal level, PrP genotype frequencies at flock level have not yet been studied. In an unmatched case-control study, three measures of flock-level prion protein (PrP) frequency estimates were investigated with respect to the scrapie status of the flock in 293 British sheep flocks (195 control flocks and 98 case flocks). Flocks with positive frequencies (more than 0 per cent) of two genotypes (VRQ/VRQ and AHQ/VRQ), large frequencies (more than 10 per cent) of the ARR/VRQ genotype, and large frequencies (more than 5.2 per cent) of the VRQ allele were at increased odds of being affected with clinical classical scrapie. When adjusted for flock size, breed and sampling strategy the genotype and allele effects remained, except that for flocks with positive frequencies of VRQ/VRQ. The known effect of increased risk with increased flock size was confirmed. A measure of the flock PrP genotype frequency profile should thus be included in studies of risk factors for scrapie. It could also be integrated into risk-based surveillance strategies for identification of "at-risk-of scrapie" flocks.

Cascade: an epidemiological model to simulate disease spread and aggregation across multiple scales in a spatial hierarchy

Disease spread occurs at several spatial scales, e.g., from field to field, plant to plant, and leaf to leaf. So far, epidemiological models have largely overlooked the multiscale nature of epidemics. Here, we propose a model that simulates disease spread across multiple scales in a nested hierarchy. The model is based on the central ideas of hierarchy theory, i.e., (i) the system is decomposed vertically into levels and horizontally into holons (elements at one level, which are complete systems when seen from the lower level), and (ii) higher levels are characterized by slower processes than lower levels. The model is individual-based, the individuals being the holons, which are either susceptible or infected. At each level, infections within one holon (i.e., infections between holons of the level below) occur independently from the other holons: infections between holons happen at the higher level. The self-similarity of the model structure and processes across all levels allows implementing the model with a simple recursive algorithm. The behavior of the model was studied using methods commonly applied to field data. Aggregation of the disease was characterized through the incidence-incidence relationship and the binomial power law, in order to study the effect of infectiousness at each level on disease aggregation. Sensitivity analyses showed that disease incidences at all levels were influenced by the infectiousness at any level, but infectiousness at higher levels had more effect than infectiousness at lower levels. It was also shown that increasing the probability of infection at a given level increased aggregation at higher level(s) and decreased aggregation at lower level(s). The results were consistent between incidence-incidence relationship and power law analysis, but the incidence-incidence relationship was more sensitive in detecting the differences in aggregation between treatments.

Dynamics of dengue epidemics in urban contexts

Dengue, similar to other arboviral diseases, exhibits complex spatiotemporal dynamics. Even at town or village level, individual-based spatially explicit models are required to correctly reproduce epidemic curves. This makes modelling at the regional level (province, country or continent) very difficult and cumbersome. We propose here a first step to build a hierarchized model by constructing a simple analytical expression which reproduces the model output from macroscopic parameters describing each 'village'. It also turns out to be a good approximation of real urban epidermic outbreaks. Subsequently, a regional model could be built by coupling these equations on a lattice.