Emulating a gravity model to infer the spatiotemporal dynamics of an infectious disease

Probabilistic models for infectious disease dynamics are useful for understanding the mechanism underlying the spread of infection. When the likelihood function for these models is expensive to evaluate, traditional likelihood-based inference may be computationally intractable. Furthermore, traditional inference may lead to poor parameter estimates and the fitted model may not capture important biological characteristics of the observed data. We propose a novel approach for resolving these issues that is inspired by recent work in emulation and calibration for complex computer models. Our motivating example is the gravity time series susceptible-infected-recovered (TSIR) model. Our approach focuses on the characteristics of the process that are of scientific interest. We find a Gaussian process approximation to the gravity model using key summary statistics obtained from model simulations. We demonstrate via simulated examples that the new approach is computationally expedient, provides accurate parameter inference, and results in a good model fit. We apply our method to analyze measles outbreaks in England and Wales in two periods, the pre-vaccination period from 1944-1965 and the vaccination period from 1966-1994. Based on our results, we are able to obtain important scientific insights about the transmission of measles. In general, our method is applicable to problems where traditional likelihood-based inference is computationally intractable or produces a poor model fit. It is also an alternative to approximate Bayesian computation (ABC) when simulations from the model are expensive.Comment: 31 pages, 8 figures and 2 table

Coexistence Patterns of Two Invasive Thistle Species, Carduus nutans and C. acanthoides, at Three Spatial Scales

To better understand the competitive processes involved in invasion by congeners, we examine coexistence patterns of two invasive species, Carduus nutans and C. acanthoides, at three spatial scales. A roadside survey of 5 × 5 km blocks in a previously identified overlap zone provided information about the regional scale. At smaller scales, we surveyed four fields of natural co-occurrence, quantifying the spatial patterns at the field scale by randomly placed 1 × 1 m quadrats and at the smallest scale by detailing plant position within the quadrats. The patterns observed are strikingly different at the different scales. At the regional scale, there is positive local autocorrelation in both species but negative cross-correlation between them, consistent with previous surveys. However, at the field scale, there is positive local autocorrelation in both species, and we generally see a positive association between the two species. At the plot scale, when excluding areas of joint absence, there is again a negative association between the two species. This pattern can also be seen at the field scale when excluding plots with joint absence. These results suggest that, at the scale of a field, the strongest factor determining location is aggregation in favorable habitats, which is a stronger force than the competition-induced segregation evidenced at small scales. Lottery competition for spatially aggregated safe sites thus appears to drive the patterns observed at the field scale, while the regional scale pattern may be a result of restricted natural dispersal and invasion history

Pathogens, Social Networks, and the Paradox of Transmission Scaling

Understanding the scaling of transmission is critical to predicting how infectious diseases will affect populations of different sizes and densities. The two classic “mean-field” epidemic models—either assuming density-dependent or frequency-dependent transmission—make predictions that are discordant with patterns seen in either within-population dynamics or across-population comparisons. In this paper, we propose that the source of this inconsistency lies in the greatly simplifying “mean-field” assumption of transmission within a fully-mixed population. Mixing in real populations is more accurately represented by a network of contacts, with interactions and infectious contacts confined to the local social neighborhood. We use network models to show that density-dependent transmission on heterogeneous networks often leads to apparent frequency dependency in the scaling of transmission across populations of different sizes. Network-methodology allows us to reconcile seemingly conflicting patterns of within- and across-population epidemiology

Slow Spread of the Aggressive Invader, Microstegium vimineum (Japanese Stiltgrass)

Microstegium vimineum (Japanese stiltgrass) is a non-native weed whose rapid invasion threatens native diversity and regeneration in forests. Using data from a 4 year experiment tracking new invasions in different habitats, we developed a spatial model of patch growth, using maximum likelihood techniques to estimate dispersal and population growth parameters. The patches expanded surprisingly slowly: in the final year, the majority of new seedlings were still within 1 m of the original patch. The influence of habitat was not as strong as anticipated, although patches created in roadside and wet meadow habitats tended to expand more rapidly and had greater reproductive ratios. The long-term projections of the patch growth model suggest much slower spread than has typically been observed for M. vimineum. The small scale of natural dispersal suggests that human-mediated dispersal, likely influenced by forest road management, is responsible for the rapid spread of this invasive species

Persistence in epidemic metapopulations: quantifying the rescue effects for measles, mumps, rubella and whooping cough

Metapopulation rescue effects are thought to be key to the persistence of many acute immunizing infections. Yet the enhancement of persistence through spatial coupling has not been previously quantified. Here we estimate the metapopulation rescue effects for four childhood infections using global WHO reported incidence data by comparing persistence on island countries vs all other countries, while controlling for key variables such as vaccine cover, birth rates and economic development. The relative risk of extinction on islands is significantly higher, and approximately double the risk of extinction in mainland countries. Furthermore, as may be expected, infections with longer infectious periods tend to have the strongest metapopulation rescue effects. Our results quantitate the notion that demography and local community size controls disease persistence

Supply chains create global benefits from improved vaccine accessibility

Ensuring a more equitable distribution of vaccines worldwide is an effective strategy to control global pandemics and support economic recovery. We analyze the socioeconomic effects - defined as health gains, lockdown-easing effect, and supply-chain rebuilding benefit - of a set of idealized COVID-19 vaccine distribution scenarios. We find that an equitable vaccine distribution across the world would increase global economic benefits by 11.7% ($950 billion per year), compared to a scenario focusing on vaccinating the entire population within vaccine-producing countries first and then distributing vaccines to non-vaccine-producing countries. With limited doses among low-income countries, prioritizing the elderly who are at high risk of dying, together with the key front-line workforce who are at high risk of exposure is projected to be economically beneficial (e.g., 0.9%~3.4% annual GDP in India). Our results reveal how equitable distributions would cascade more protection of vaccines to people and ways to improve vaccine equity and accessibility globally through international collaboration

Seven challenges in modeling vaccine preventable diseasesC

Vaccination has been one of the most successful public health measures since the introduction of basic sanitation. Substantial mortality and morbidity reductions have been achieved via vaccination against many infections, and the list of diseases that are potentially controllable by vaccines is growing steadily. We introduce key challenges for modelling in shaping our understanding and guiding policy decisions related to vaccine preventable diseases