When should lockdown be implemented? Devising cost-effective strategies for managing epidemics amid vaccine uncertainty.

During an infectious disease outbreak, public health policy makers are tasked with strategically implementing interventions whilst balancing competing objectives. To provide a quantitative framework that can be used to guide these decisions, it is helpful to devise a clear and specific objective function that can be evaluated to determine the optimal outbreak response. In this study, we have developed a mathematical modelling framework representing outbreaks of a novel emerging pathogen for which non-pharmaceutical interventions (NPIs) are imposed or removed based on thresholds for hospital occupancy. These thresholds are set at different levels to define four unique strategies for disease control. We illustrate that the optimal intervention strategy is contingent on the choice of objective function. Specifically, the optimal strategy depends on the extent to which policy makers prioritise reducing health costs due to infection over the costs associated with maintaining interventions. Motivated by the scenario early in the COVID-19 pandemic, we incorporate the development of a vaccine into our modelling framework and demonstrate that a policy maker's belief about when a vaccine will become available in future, and its eventual coverage (and/or effectiveness), affects the optimal strategy to adopt early in the outbreak. Furthermore, we show how uncertainty in these quantities can be accounted for when deciding which interventions to introduce. This research highlights the benefits of policy makers being explicit about the precise objectives of introducing interventions.

Modeling target-density-based cull strategies to contain foot-and-mouth disease outbreaks.

Total ring depopulation is sometimes used as a management strategy for emerging infectious diseases in livestock, which raises ethical concerns regarding the potential slaughter of large numbers of healthy animals. We evaluated a farm-density-based ring culling strategy to control foot-and-mouth disease (FMD) in the United Kingdom (UK), which may allow for some farms within rings around infected premises (IPs) to escape depopulation. We simulated this reduced farm density, or "target density", strategy using a spatially-explicit, stochastic, state-transition algorithm. We modeled FMD spread in four counties in the UK that have different farm demographics, using 740,000 simulations in a full-factorial analysis of epidemic impact measures (i.e., culled animals, culled farms, and epidemic length) and cull strategy parameters (i.e., target farm density, daily farm cull capacity, and cull radius). All of the cull strategy parameters listed above were drivers of epidemic impact. Our simulated target density strategy was usually more effective at combatting FMD compared with traditional total ring depopulation when considering mean culled animals and culled farms and was especially effective when daily farm cull capacity was low. The differences in epidemic impact measures among the counties are likely driven by farm demography, especially differences in cattle and farm density. To prevent over-culling and the associated economic, organizational, ethical, and psychological impacts, the target density strategy may be worth considering in decision-making processes for future control of FMD and other diseases.

Identification of dynamical changes of rabies transmission under quarantine: Community-based measures towards rabies elimination.

Quarantine has been long used as a public health response to emerging infectious diseases, particularly at the onset of an epidemic when the infected proportion of a population remains identifiable and logistically tractable. In theory, the same logic should apply to low-incidence infections; however, the application and impact of quarantine in low prevalence settings appears less common and lacks a formal analysis. Here, we present a quantitative framework using a series of progressively more biologically realistic models of canine rabies in domestic dogs and from dogs to humans, a suitable example system to characterize dynamical changes under varying levels of dog quarantine. We explicitly incorporate health-seeking behaviour data to inform the modelling of contact-tracing and exclusion of rabies suspect and probable dogs that can be identified through bite-histories of patients presenting at anti-rabies clinics. We find that a temporary quarantine of rabies suspect and probable dogs provides a powerful tool to curtail rabies transmission, especially in settings where optimal vaccination coverage is yet to be achieved, providing a critical stopgap to reduce the number of human and animal deaths due to rabid bites. We conclude that whilst comprehensive measures including sensitive surveillance and large-scale vaccination of dogs will be required to achieve disease elimination and sustained freedom given the persistent risk of rabies re-introductions, quarantine offers a low-cost community driven solution to intersectoral health burden.

Modelling seasonality of Lassa fever incidences and vector dynamics in Nigeria.

Lassa fever (Lf) is a viral haemorrhagic disease endemic to West Africa and is caused by the Lassa mammarenavirus. The rodent Mastomys natalensis serves as the primary reservoir and its ecology and behaviour have been linked to the distinct spatial and temporal patterns in the incidence of Lf. Nigeria has experienced an unprecedented epidemic that lasted from January until April of 2018, which has been followed by subsequent epidemics of Lf in the same period every year since. While previous research has modelled the case seasonality within Nigeria, this did not capture the seasonal variation in the reproduction of the zoonotic reservoir and its effect on case numbers. To this end, we introduce an approximate Bayesian computation scheme to fit our model to the case data from 2018-2020 supplied by the NCDC. In this study we used a periodically forced seasonal nonautonomous system of ordinary differential equations as a vector model to demonstrate that the population dynamics of the rodent reservoir may be responsible for the spikes in the number of observed cases in humans. The results show that in December through to March, spillover from the zoonotic reservoir drastically increases and spreads the virus to the people of Nigeria. Therefore to effectively combat Lf, attention and efforts should be concentrated during this period.

Spatio-temporal surveillance and early detection of SARS-CoV-2 variants of concern: a retrospective analysis.

The SARS-CoV-2 pandemic has been characterized by the repeated emergence of genetically distinct virus variants of increased transmissibility and immune evasion compared to pre-existing lineages. In many countries, their containment required the intervention of public health authorities and the imposition of control measures. While the primary role of testing is to identify infection, target treatment, and limit spread (through isolation and contact tracing), a secondary benefit is in terms of surveillance and the early detection of new variants. Here we study the spatial invasion and early spread of the Alpha, Delta and Omicron (BA.1 and BA.2) variants in England from September 2020 to February 2022 using the random neighbourhood covering (RaNCover) method. This is a statistical technique for the detection of aberrations in spatial point processes, which we tailored here to community PCR (polymerase-chain-reaction) test data where the TaqPath kit provides a proxy measure of the switch between variants. Retrospectively, RaNCover detected the earliest signals associated with the four novel variants that led to large infection waves in England. With suitable data our method therefore has the potential to rapidly detect outbreaks of future SARS-CoV-2 variants, thus helping to inform targeted public health interventions.

Modelling African horse sickness emergence and transmission in the South African control area using a deterministic metapopulation approach.

African horse sickness is an equine orbivirus transmitted by Culicoides Latreille biting midges. In the last 80 years, it has caused several devastating outbreaks in the equine population in Europe, the Far and Middle East, North Africa, South-East Asia, and sub-Saharan Africa. The disease is endemic in South Africa; however, a unique control area has been set up in the Western Cape where increased surveillance and control measures have been put in place. A deterministic metapopulation model was developed to explore if an outbreak might occur, and how it might develop, if a latently infected horse was to be imported into the control area, by varying the geographical location and months of import. To do this, a previously published ordinary differential equation model was developed with a metapopulation approach and included a vaccinated horse population. Outbreak length, time to peak infection, number of infected horses at the peak, number of horses overall affected (recovered or dead), re-emergence, and Rv (the basic reproduction number in the presence of vaccination) were recorded and displayed using GIS mapping. The model predictions were compared to previous outbreak data to ensure validity. The warmer months (November to March) had longer outbreaks than the colder months (May to September), took more time to reach the peak, and had a greater total outbreak size with more horses infected at the peak. Rv appeared to be a poor predictor of outbreak dynamics for this simulation. A sensitivity analysis indicated that control measures such as vaccination and vector control are potentially effective to manage the spread of an outbreak, and shortening the vaccination window to July to September may reduce the risk of vaccine-associated outbreaks.

Incorporating heterogeneity in farmer disease control behaviour into a livestock disease transmission model.

Human behaviour is critical to effective responses to livestock disease outbreaks, especially with respect to vaccination uptake. Traditionally, mathematical models used to inform this behaviour have not taken heterogeneity in farmer behaviour into account. We address this by exploring how heterogeneity in farmers vaccination behaviour can be incorporated to inform mathematical models. We developed and used a graphical user interface to elicit farmers (n = 60) vaccination decisions to an unfolding fast-spreading epidemic and linked this to their psychosocial and behavioural profiles. We identified, via cluster analysis, robust patterns of heterogeneity in vaccination behaviour. By incorporating these vaccination behavioural groupings into a mathematical model for a fast-spreading livestock infection, using computational simulation we explored how the inclusion of heterogeneity in farmer disease control behaviour may impact epidemiological and economic focused outcomes. When assuming homogeneity in farmer behaviour versus configurations informed by the psychosocial profile cluster estimates, the modelled scenarios revealed a disconnect in projected distributions and threshold statistics across outbreak size, outbreak duration and economic metrics.

Emergence of SARS-CoV-2 Delta Variant and Effect of Nonpharmaceutical Interventions, British Columbia, Canada.

In British Columbia, Canada, initial growth of the SARS-CoV-2 Delta variant was slower than that reported in other jurisdictions. Delta became the dominant variant (>50% prevalence) within ≈7-13 weeks of first detection in regions within the United Kingdom and United States. In British Columbia, it remained at <10% of weekly incident COVID-19 cases for 13 weeks after first detection on March 21, 2021, eventually reaching dominance after 17 weeks. We describe the growth of Delta variant cases in British Columbia during March 1-June 30, 2021, and apply retrospective counterfactual modeling to examine factors for the initially low COVID-19 case rate after Delta introduction, such as vaccination coverage and nonpharmaceutical interventions. Growth of COVID-19 cases in the first 3 months after Delta emergence was likely limited in British Columbia because additional nonpharmaceutical interventions were implemented to reduce levels of contact at the end of March 2021, soon after variant emergence.

Coughs, colds and "freshers' flu" survey in the University of Cambridge, 2007-2008.

Universities provide many opportunities for the spread of infectious respiratory illnesses. Students are brought together into close proximity from all across the world and interact with one another in their accommodation, through lectures and small group teaching and in social settings. The COVID-19 global pandemic has highlighted the need for sufficient data to help determine which of these factors are important for infectious disease transmission in universities and hence control university morbidity as well as community spillover. We describe the data from a previously unpublished self-reported university survey of coughs, colds and influenza-like symptoms collected in Cambridge, UK, during winter 2007-2008. The online survey collected information on symptoms and socio-demographic, academic and lifestyle factors. There were 1076 responses, 97% from University of Cambridge students (5.7% of the total university student population), 3% from staff and <1% from other participants, reporting onset of symptoms between September 2007 and March 2008. Undergraduates are seen to report symptoms earlier in the term than postgraduates; differences in reported date of symptoms are also seen between subjects and accommodation types, although these descriptive results could be confounded by survey biases. Despite the historical and exploratory nature of the study, this is one of few recent detailed datasets of influenza-like infection in a university context and is especially valuable to share now to improve understanding of potential transmission dynamics in universities during the current COVID-19 pandemic.

Modelling the impact of non-pharmaceutical interventions on the spread of COVID-19 in Saudi Arabia.

Countries around the world have implemented a series of interventions to contain the pandemic of coronavirus disease (COVID-19), and significant lessons can be drawn from the study of the full transmission dynamics of the disease caused by-severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-in the Eastern, Madinah, Makkah, and Riyadh regions of Saudi Arabia, where robust non-pharmaceutical interventions effectively suppressed the local outbreak of this disease. On the basis of 333732 laboratory-confirmed cases, we used mathematical modelling to reconstruct the complete spectrum dynamics of COVID-19 in Saudi Arabia between 2 March and 25 September 2020 over 5 periods characterised by events and interventions. Our model account for asymptomatic and presymptomatic infectiousness, time-varying ascertainable infection rate, and transmission rates. Our results indicate that non-pharmaceutical interventions were effective in containing the epidemic, with reproduction numbers decreasing on average to 0.29 (0.19-0.66) in the Eastern, Madinah, Makkah, and Riyadh region. The chance of resurgence after the lifting of all interventions after 30 consecutive days with no symptomatic cases is also examined and emphasizes the danger presented by largely hidden infections while switching control strategies. These findings have major significance for evaluating methods for maintaining monitoring and interventions to eventually reduce outbreaks of COVID-19 in Saudi Arabia in the future.

An exploration of within-herd dynamics of a transboundary livestock disease: A foot and mouth disease case study.

Transboundary livestock diseases are a high priority for policy makers because of the serious economic burdens associated with infection. In order to make well informed preparedness and response plans, policy makers often utilize mathematical models to understand possible outcomes of different control strategies and outbreak scenarios. Many of these models focus on the transmission between herds and the overall trajectory of the outbreak. While the course of infection within herds has not been the focus of the majority of models, a thorough understanding of within-herd dynamics can provide valuable insight into a disease system by providing information on herd-level biological properties of the infection, which can be used to inform decision making in both endemic and outbreak settings and to inform larger between-herd models. In this study, we develop three stochastic simulation models to study within-herd foot and mouth disease dynamics and the implications of different empirical data-based assumptions about the timing of the onset of infectiousness and clinical signs. We also study the influence of herd size and the proportion of the herd that is initially infected on the outcome of the infection. We find that increasing herd size increases the duration of infectiousness and that the size of the herd plays a more significant role in determining this duration than the number of initially infected cattle in that herd. We also find that the assumptions made regarding the onset of infectiousness and clinical signs, which are based on contradictory empirical findings, can result in the predictions about when infection would be detectable differing by several days. Therefore, the disease progression used to characterize the course of infection in a single bovine host could have significant implications for determining when herds can be detected and subsequently controlled; the timing of which could influence the overall predicted trajectory of outbreaks.

The Importance of Livestock Demography and Infrastructure in Driving Foot and Mouth Disease Dynamics.

Transboundary animal diseases, such as foot and mouth disease (FMD) pose a significant and ongoing threat to global food security. Such diseases can produce large, spatially complex outbreaks. Mathematical models are often used to understand the spatio-temporal dynamics and create response plans for possible disease introductions. Model assumptions regarding transmission behavior of premises and movement patterns of livestock directly impact our understanding of the ecological drivers of outbreaks and how to best control them. Here, we investigate the impact that these assumptions have on model predictions of FMD outbreaks in the U.S. using models of livestock shipment networks and disease spread. We explore the impact of changing assumptions about premises transmission behavior, both by including within-herd dynamics, and by accounting for premises type and increasing the accuracy of shipment predictions. We find that the impact these assumptions have on outbreak predictions is less than the impact of the underlying livestock demography, but that they are important for investigating some response objectives, such as the impact on trade. These results suggest that demography is a key ecological driver of outbreaks and is critical for making robust predictions but that understanding management objectives is also important when making choices about model assumptions.

Retrospectively modeling the effects of increased global vaccine sharing on the COVID-19 pandemic.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has caused considerable morbidity and mortality worldwide. The protection provided by vaccines and booster doses offered a method of mitigating severe clinical outcomes and mortality. However, by the end of 2021, the global distribution of vaccines was highly heterogeneous, with some countries gaining over 90% coverage in adults, whereas others reached less than 2%. In this study, we used an age-structured model of SARS-CoV-2 dynamics, matched to national data from 152 countries in 2021, to investigate the global impact of different potential vaccine sharing protocols that attempted to address this inequity. We quantified the effects of implemented vaccine rollout strategies on the spread of SARS-CoV-2, the subsequent global burden of disease and the emergence of novel variants. We found that greater vaccine sharing would have lowered the total global burden of disease, and any associated increases in infections in previously vaccine-rich countries could have been mitigated by reduced relaxation of non-pharmaceutical interventions. Our results reinforce the health message, pertinent to future pandemics, that vaccine distribution proportional to wealth, rather than to need, may be detrimental to all.

A comparative analysis of epidemiological characteristics of MERS-CoV and SARS-CoV-2 in Saudi Arabia.

In this study, we determine and compare the incubation duration, serial interval, pre-symptomatic transmission, and case fatality rate of MERS-CoV and COVID-19 in Saudi Arabia based on contact tracing data we acquired in Saudi Arabia. The date of infection and infector-infectee pairings are deduced from travel history to Saudi Arabia or exposure to confirmed cases. The incubation times and serial intervals are estimated using parametric models accounting for exposure interval censoring. Our estimations show that MERS-CoV has a mean incubation time of 7.21 (95% CI: 6.59-7.85) days, whereas COVID-19 (for the circulating strain in the study period) has a mean incubation period of 5.43(95% CI: 4.81-6.11) days. MERS-CoV has an estimated serial interval of 14.13(95% CI: 13.9-14.7) days, while COVID-19 has an estimated serial interval of 5.1(95% CI: 5.0-5.5) days. The COVID-19 serial interval is found to be shorter than the incubation time, indicating that pre-symptomatic transmission may occur in a significant fraction of transmission events. We conclude that during the COVID-19 wave studied, at least 75% of transmission happened prior to the onset of symptoms. The CFR for MERS-CoV is estimated to be 38.1% (95% CI: 36.8-39.5), while the CFR for COVID-19 1.67% (95% CI: 1.63-1.71). This work is expected to help design future surveillance and intervention program targeted at specific respiratory virus outbreaks, and have implications for contingency planning for future coronavirus outbreaks.

Vote-processing rules for combining control recommendations from multiple models.

Mathematical modelling is used during disease outbreaks to compare control interventions. Using multiple models, the best method to combine model recommendations is unclear. Existing methods weight model projections, then rank control interventions using the combined projections, presuming model outputs are directly comparable. However, the way each model represents the epidemiological system will vary. We apply electoral vote-processing rules to combine model-generated rankings of interventions. Combining rankings of interventions, instead of combining model projections, avoids assuming that projections are comparable as all comparisons of projections are made within each model. We investigate four rules: First-past-the-post, Alternative Vote (AV), Coombs Method and Borda Count. We investigate rule sensitivity by including models that favour only one action or including those that rank interventions randomly. We investigate two case studies: the 2014 Ebola outbreak in West Africa (37 compartmental models) and a hypothetical foot-and-mouth disease outbreak in UK (four individual-based models). The Coombs Method was least susceptible to adding models that favoured a single action, Borda Count and AV were most susceptible to adding models that ranked interventions randomly. Each rule chose the same intervention as when ranking interventions by mean projections, suggesting that combining rankings provides similar recommendations with fewer assumptions about model comparability. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Optimal health and economic impact of non-pharmaceutical intervention measures prior and post vaccination in England: a mathematical modelling study.

Background. Even with good progress on vaccination, SARS-CoV-2 infections in the UK may continue to impose a high burden of disease and therefore pose substantial challenges for health policy decision makers. Stringent government-mandated physical distancing measures (lockdown) have been demonstrated to be epidemiologically effective, but can have both positive and negative economic consequences. The duration and frequency of any intervention policy could, in theory, be optimized to maximize economic benefits while achieving substantial reductions in disease. Methods. Here, we use a pre-existing SARS-CoV-2 transmission model to assess the health and economic implications of different strengths of control through time in order to identify optimal approaches to non-pharmaceutical intervention stringency in the UK, considering the role of vaccination in reducing the need for future physical distancing measures. The model is calibrated to the COVID-19 epidemic in England and we carry out retrospective analysis of the optimal timing of precautionary breaks in 2020 and the optimal relaxation policy from the January 2021 lockdown, considering the willingness to pay (WTP) for health improvement. Results. We find that the precise timing and intensity of interventions is highly dependent upon the objective of control. As intervention measures are relaxed, we predict a resurgence in cases, but the optimal intervention policy can be established dependent upon the WTP per quality adjusted life year loss avoided. Our results show that establishing an optimal level of control can result in a reduction in net monetary loss of billions of pounds, dependent upon the precise WTP value. Conclusion. It is vital, as the UK emerges from lockdown, but continues to face an on-going pandemic, to accurately establish the overall health and economic costs when making policy decisions. We demonstrate how some of these can be quantified, employing mechanistic infectious disease transmission models to establish optimal levels of control for the ongoing COVID-19 pandemic.

Non-pharmaceutical interventions and their relevance in the COVID-19 vaccine rollout in Saudi Arabia and Arab Gulf countries.

In the early stages of the pandemic, Saudi Arabia and other countries in the Arab Gulf region relied on non-pharmaceutical therapies to limit the effect of the pandemic, much like other nations across the world. In comparison to other nations in the area or globally, these interventions were successful at lowering the healthcare burden. This was accomplished via the deterioration of the economy, education, and a variety of other societal activities. By the end of 2020, the promise of effective vaccinations against SARS-CoV-2 have been realized, and vaccination programs have begun in developed countries, followed by the rest of the world. Despite this, there is still a long way to go in the fight against the disease. In order to explore disease transmission, vaccine rollout and prioritisation, as well as behavioural dynamics, we relied on an age-structured compartmental model. We examine how individual and social behaviour changes in response to the initiation of vaccination campaigns and the relaxation of non-pharmacological treatments. Overall, vaccination remains the most effective method of containing the disease and resuming normal life. Additionally, we evaluate several vaccination prioritisation schemes based on age group, behavioural responses, vaccine effectiveness, and vaccination rollout speed. We applied our model to four Arab Gulf nations (Saudi Arabia, Bahrain, the United Arab Emirates, and Oman), which were chosen for their low mortality rate compared to other countries in the region or worldwide, as well as their demographic and economic settings. We fitted the model using actual pandemic data in these countries. Our results suggest that vaccinations focused on the elderly and rapid vaccine distribution are critical for reducing disease resurgence. Our result also reinforces the cautious note that early relaxation of safety measures may compromise the vaccine's short-term advantages.

Cattle transport network predicts endemic and epidemic foot-and-mouth disease risk on farms in Turkey.

The structure of contact networks affects the likelihood of disease spread at the population scale and the risk of infection at any given node. Though this has been well characterized for both theoretical and empirical networks for the spread of epidemics on completely susceptible networks, the long-term impact of network structure on risk of infection with an endemic pathogen, where nodes can be infected more than once, has been less well characterized. Here, we analyze detailed records of the transportation of cattle among farms in Turkey to characterize the global and local attributes of the directed-weighted shipments network between 2007-2012. We then study the correlations between network properties and the likelihood of infection with, or exposure to, foot-and-mouth disease (FMD) over the same time period using recorded outbreaks. The shipments network shows a complex combination of features (local and global) that have not been previously reported in other networks of shipments; i.e. small-worldness, scale-freeness, modular structure, among others. We find that nodes that were either infected or at high risk of infection with FMD (within one link from an infected farm) had disproportionately higher degree, were more central (eigenvector centrality and coreness), and were more likely to be net recipients of shipments compared to those that were always more than 2 links away from an infected farm. High in-degree (i.e. many shipments received) was the best univariate predictor of infection. Low in-coreness (i.e. peripheral nodes) was the best univariate predictor of nodes always more than 2 links away from an infected farm. These results are robust across the three different serotypes of FMD observed in Turkey and during periods of low-endemic prevalence and high-prevalence outbreaks.

Comparison of the 2021 COVID-19 roadmap projections against public health data in England.

Control and mitigation of the COVID-19 pandemic in England has relied on a combination of vaccination and non-pharmaceutical interventions (NPIs). Some of these NPIs are extremely costly (economically and socially), so it was important to relax these promptly without overwhelming already burdened health services. The eventual policy was a Roadmap of four relaxation steps throughout 2021, taking England from lock-down to the cessation of all restrictions on social interaction. In a series of six Roadmap documents generated throughout 2021, models assessed the potential risk of each relaxation step. Here we show that the model projections generated a reliable estimation of medium-term hospital admission trends, with the data points up to September 2021 generally lying within our 95% prediction intervals. The greatest uncertainties in the modelled scenarios came from vaccine efficacy estimates against novel variants, and from assumptions about human behaviour in the face of changing restrictions and risk.