Approximating steady state distributions for household structured epidemic models.

Household-structured infectious disease models consider the increased transmission potential between individuals of the same household when compared with two individuals in different households. Accounting for these heterogeneities in transmission enables control measures to be more effectively planned. Ideally, pre-control data may be used to fit such a household-structured model at an endemic steady state, before making dynamic forward-predictions under different proposed strategies. However, this requires the accurate calculation of the steady states for the full dynamic model. We observe that steady state SIS dynamics with household structure cannot necessarily be described by the master equation for a single household, instead requiring consideration of the full system. However, solving the full system of equations becomes increasingly computationally intensive, particularly for higher-dimensional models. We compare two approximations to the full system: the single household master equation; and a proposed alternative method, using the Fokker-Planck equation. Moment closure is another commonly used method, but for more complicated systems, the equations quickly become unwieldy and very difficult to derive. In comparison, using the master equation for a single household is easily implementable, however it can be quite inaccurate. In this paper we compare these methods in terms of accuracy and ease of implementation. We find that there are regions of parameter space in which each method outperforms the other, and that these regions of parameter space can be characterised by the infection prevalence, or by the correlation between household states.

Climate drivers of plague epidemiology in British India, 1898-1949.

Plague, caused by Yersinia pestis infection, continues to threaten low- and middle-income countries throughout the world. The complex interactions between rodents and fleas with their respective environments challenge our understanding of human plague epidemiology. Historical long-term datasets of reported plague cases offer a unique opportunity to elucidate the effects of climate on plague outbreaks in detail. Here, we analyse monthly plague deaths and climate data from 25 provinces in British India from 1898 to 1949 to generate insights into the influence of temperature, rainfall and humidity on the occurrence, severity and timing of plague outbreaks. We find that moderate relative humidity levels of between 60% and 80% were strongly associated with outbreaks. Using wavelet analysis, we determine that the nationwide spread of plague was driven by changes in humidity, where, on average, a one-month delay in the onset of rising humidity translated into a one-month delay in the timing of plague outbreaks. This work can inform modern spatio-temporal predictive models for the disease and aid in the development of early-warning strategies for the deployment of prophylactic treatments and other control measures.

Modelling the persistence and control of Rift Valley fever virus in a spatially heterogeneous landscape.

The persistence mechanisms of Rift Valley fever (RVF), a zoonotic arboviral haemorrhagic fever, at both local and broader geographical scales have yet to be fully understood and rigorously quantified. We developed a mathematical metapopulation model describing RVF virus transmission in livestock across the four islands of the Comoros archipelago, accounting for island-specific environments and inter-island animal movements. By fitting our model in a Bayesian framework to 2004-2015 surveillance data, we estimated the importance of environmental drivers and animal movements on disease persistence, and tested the impact of different control scenarios on reducing disease burden throughout the archipelago. Here we report that (i) the archipelago network was able to sustain viral transmission in the absence of explicit disease introduction events after early 2007, (ii) repeated outbreaks during 2004-2020 may have gone under-detected by local surveillance, and (iii) co-ordinated within-island control measures are more effective than between-island animal movement restrictions.