Disease Emergence in Multi-Patch Stochastic Epidemic Models with Demographic and Seasonal Variability

The impacts of spatial-temporal heterogeneity of human-to-human contacts on the extinction probability of infectious disease from branching process model

In this study, we focus on the impacts of spatial-temporal heterogeneity of human-to-human contacts on the spread of infectious diseases and develop a multi-type branching process model by introducing random human-to-human contact mode into a structured population. We provide the general formulas of the generation size, extinction probability, and basic reproduction number of the proposed branching process model. The result shows that the natural temporal heterogeneity (i.e. random contacts over time) can lead to a higher extinction probability while remains the same basic reproduction number and generation size. This is also numerically verified by choosing the real contact distributions from different circumstances of four countries. In addition, we observe a non-monotonic pattern of the differences, against the transmission probability and the mean contact rate, between the extinction probabilities under the constant and random contact patterns. Given the spatial heterogeneity, we show that it can contribute to the increase of basic reproduction number, but also increase the extinction probability of the infectious disease. This study adds novel insights to the course of the impact of heterogeneity on the transmission dynamics and also provides additional evidence for the limited role of reproduction numbers.

A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments

Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t=t₀, assuming that environmental conditions remain identical from that time onwards (i.e. for all t≥t₀). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t=t₀, accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameters vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens.

Determining the effects of wind-aided midge movement on the outbreak and coexistence of multiple bluetongue virus serotypes in patchy environments

Bluetongue virus (BTV) has 27 serotypes with some of them coexisting in different environments which make its control difficult. Wind-aided midge movement is a known mechanism in the spread of BTV. However, its effects on the dynamics of multiple BTV serotypes are not clear. Ordinary differential equation (ODE) and continuous-time Markov chain (CTMC) models for two BTV serotypes in an environment divided into two patches depending on the risk of infection are formulated and analysed. By approximating the CTMC model with a multitype branching process, an estimate for the probability of a major outbreak of two BTV serotypes is obtained. It is shown that without movement a major outbreak occurs in the high-risk patch, but with cattle or midge movement it occurs in both patches. When a major outbreak occurs, numerical simulations of the ODE model illustrate possible coexistence in both patches if the patches are connected by midge or cattle movement. Sensitivity analysis, based on the Latin hypercube sampling method, identified midge mortality and biting rates as being the most important in determining the magnitude of the probability of a major outbreak. These results indicate the significance of wind-aided midge movement on the outbreak and coexistence of multiple BTV serotypes in patchy environments.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed.

Methods

Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel.

Results

We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility.

Conclusions

Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain.

Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.

Probability of a zoonotic spillover with seasonal variation

Zoonotic infectious diseases are spread from animals to humans. It is estimated that over 60% of human infectious diseases are zoonotic and 75% of them are emerging zoonoses. The majority of emerging zoonotic infectious diseases are caused by viruses including avian influenza, rabies, Ebola, coronaviruses and hantaviruses. Spillover of infection from animals to humans depends on a complex transmission pathway, which is influenced by epidemiological and environmental processes. In this investigation, the focus is on direct transmission between animals and humans and the effects of seasonal variations on the transmission and recovery rates. Fluctuations in transmission and recovery, besides being influenced by physiological processes and behaviors of pathogen and host, are driven by seasonal variations in temperature, humidity or rainfall. A new time-nonhomogeneous stochastic process is formulated for infectious disease spread from animals to humans when transmission and recovery rates are time-periodic. A branching process approximation is applied near the disease-free state to predict the probability of the first spillover event from animals to humans. This probability is a periodic function of the time when infection is introduced into the animal population. It is shown that the highest risk of a spillover depends on a combination of animal to human transmission, animal to animal transmission and animal recovery. The results are applied to a stochastic model for avian influenza with spillover from domestic poultry to humans.