Rapid simulation of spatial epidemics: a spectral method

Dynamics of COVID-19 transmission with comorbidity: a data driven modelling based approach

An outbreak of the COVID-19 pandemic is a major public health disease as well as a challenging task to people with comorbidity worldwide. According to a report, comorbidity enhances the risk factors with complications of COVID-19. Here, we propose and explore a mathematical framework to study the transmission dynamics of COVID-19 with comorbidity. Within this framework, the model is calibrated by using new daily confirmed COVID-19 cases in India. The qualitative properties of the model and the stability of feasible equilibrium are studied. The model experiences the scenario of backward bifurcation by parameter regime accounting for progress in susceptibility to acquire infection by comorbidity individuals. The endemic equilibrium is asymptotically stable if recruitment of comorbidity becomes higher without acquiring the infection. Moreover, a larger backward bifurcation regime indicates the possibility of more infection in susceptible individuals. A dynamics in the mean fluctuation of the force of infection is investigated with different parameter regimes. A significant correlation is established between the force of infection and corresponding Shannon entropy under the same parameters, which provides evidence that infection reaches a significant proportion of the susceptible.

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R₀) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley’s K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R₀ was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R₀ and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches.

When modeling the spread of infectious livestock diseases such as foot-and-mouth disease (FMD), the distance between premises is an important aspect. In the U.S., locations of premises are not available, forcing modelers to make assumptions about their coordinates. Such assumptions can be more or less crude and will impact the conclusions drawn from the model. To investigate the impact of such assumptions, we modeled outbreaks of FMD within the cattle population of the U.S. under two assumptions about premises locations. Their position was either randomly distributed within counties or informed by a state-of-the-art method developed specifically to simulate realistic locations of agricultural operations. We found that the higher degree of spatial clustering of premises associated with more realistic assumptions about locations leads to a substantially higher risk of outbreaks. Our results also show that the amount with which the risk is under-estimated by randomizing locations is unevenly distributed across the landscape. Together, these findings show a clear support for using informed methods to determine the spatial locations of premises and highlight the importance of spatial clustering when modeling FMD-like diseases.

Need for speed: An optimized gridding approach for spatially explicit disease simulations

Numerical models for simulating outbreaks of infectious diseases are powerful tools for informing surveillance and control strategy decisions. However, large-scale spatially explicit models can be limited by the amount of computational resources they require, which poses a problem when multiple scenarios need to be explored to provide policy recommendations. We introduce an easily implemented method that can reduce computation time in a standard Susceptible-Exposed-Infectious-Removed (SEIR) model without introducing any further approximations or truncations. It is based on a hierarchical infection process that operates on entire groups of spatially related nodes (cells in a grid) in order to efficiently filter out large volumes of susceptible nodes that would otherwise have required expensive calculations. After the filtering of the cells, only a subset of the nodes that were originally at risk are then evaluated for actual infection. The increase in efficiency is sensitive to the exact configuration of the grid, and we describe a simple method to find an estimate of the optimal configuration of a given landscape as well as a method to partition the landscape into a grid configuration. To investigate its efficiency, we compare the introduced methods to other algorithms and evaluate computation time, focusing on simulated outbreaks of foot-and-mouth disease (FMD) on the farm population of the USA, the UK and Sweden, as well as on three randomly generated populations with varying degree of clustering. The introduced method provided up to 500 times faster calculations than pairwise computation, and consistently performed as well or better than other available methods. This enables large scale, spatially explicit simulations such as for the entire continental USA without sacrificing realism or predictive power.

Numerical models for simulating the outbreak of infectious disease are powerful tools that can be used to inform policy decisions by simulating outbreaks and control actions. However, they rely on considerable computational power to explore all outcomes and scenarios of interest. Focusing on model types commonly used for livestock diseases, we here introduce novel algorithms for efficient computation, alongside techniques to optimize them based on simplifying assumptions. Through simulations of FMD outbreak in the US, the UK and Sweden, as well as in computer generated landscapes, we test how these methods perform under realistic conditions. We find that our optimization techniques works well, and when the introduced algorithms are implemented with these optimizations, computation time can be reduced by more than two orders of magnitude compared to pairwise calculations. We propose that the considered algorithms—which are straight forward to implement—will be useful for simulation of a wide range of diseases, and will promote the use of simulation models for policy recommendation.