Resolving the enigma of Iquitos and Manaus: A modeling analysis of multiple COVID-19 epidemic waves in two Amazonian cities.

The two nearby Amazonian cities of Iquitos and Manaus endured explosive COVID-19 epidemics and may well have suffered the world's highest infection and death rates over 2020, the first year of the pandemic. State-of-the-art epidemiological and modeling studies estimated that the populations of both cities came close to attaining herd immunity (>70% infected) at the termination of the first wave and were thus protected. This makes it difficult to explain the more deadly second wave of COVID-19 that struck again in Manaus just months later, simultaneous with the appearance of a new P.1 variant of concern, creating a catastrophe for the unprepared population. It was suggested that the second wave was driven by reinfections, but the episode has become controversial and an enigma in the history of the pandemic. We present a data-driven model of epidemic dynamics in Iquitos, which we also use to explain and model events in Manaus. By reverse engineering the multiple epidemic waves over 2 y in these two cities, the partially observed Markov process model inferred that the first wave left Manaus with a highly susceptible and vulnerable population (≈40% infected) open to invasion by P.1, in contrast to Iquitos (≈72% infected). The model reconstructed the full epidemic outbreak dynamics from mortality data by fitting a flexible time-varying reproductive number [Formula: see text] while estimating reinfection and impulsive immune evasion. The approach is currently highly relevant given the lack of tools available to assess these factors as new SARS-CoV-2 virus variants appear with different degrees of immune evasion.

The immune evasion ability of Delta variant is comparable to that of Beta variant in South Africa.

BACKGROUND: The high immune evasion ability of SARS-COV-2 Omicron variant surprised the world and appears to be far stronger than any previous variant. Previous to Omicron it has been difficult to assess and compare immune evasion ability of different variants, including the Beta and Delta variants, because of the relatively small numbers of reinfections and because of the problems in correctly identifying reinfections in the population. This has led to different claims appearing in the literature. Thus we find claims of both high and low immune evasion for the Beta variant. Some findings have suggested that the Beta variant has a higher immune evasion ability than the Delta variant in South Africa, and others that it has a lower ability. METHOD: In this brief report, we re-analyse a unique dataset of variant-specific reinfection data and a simple model to correct for the infection attack rates of different variants. RESULT: We find that a model with the Delta variant having  an equal or higher immune evasion ability than Beta variant is compatible with the data. CONCLUSION: We conclude that the immune evasion ability of Beta variant is not stronger than Delta variant, and indeed, the immune evasion abilities of both variants are weak in South Africa.

Evaluation of Effectiveness of Global COVID-19 Vaccination Campaign.

To model estimated deaths averted by COVID-19 vaccines, we used state-of-the-art mathematical modeling, likelihood-based inference, and reported COVID-19 death and vaccination data. We estimated that >1.5 million deaths were averted in 12 countries. Our model can help assess effectiveness of the vaccination program, which is crucial for curbing the COVID-19 pandemic.

Post-lockdown abatement of COVID-19 by fast periodic switching.

COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show-as proof of concept grounded on rigorous mathematical evidence-that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn-while not eliminating the virus-this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github at https://github.com/V4p1d/FPSP_Covid19. A software tool has also been developed so that interested parties can explore the proof-of-concept system.

Network motifs and their origins.

Modern network science is a new and exciting research field that has transformed the study of complex systems over the last 2 decades. Of particular interest is the identification of small "network motifs" that might be embedded in a larger network and that indicate the presence of evolutionary design principles or have an overly influential role on system-wide dynamics. Motifs are patterns of interconnections, or subgraphs, that appear in an observed network significantly more often than in compatible randomized networks. The concept of network motifs was introduced into Systems Biology by Milo, Alon and colleagues in 2002, quickly revolutionized the field, and it has had a huge impact in wider scientific domains ever since. Here, we argue that the same concept and tools for the detection of motifs were well known in the ecological literature decades into the last century, a fact that is generally not recognized. We review the early history of network motifs, their evolution in the mathematics literature, and their recent rediscoveries.

Inferring about the extinction of a species using certain and uncertain sightings.

The sighting record of threatened species is often used to infer the possibility of extinction. Most of these sightings have uncertain validity. Solow and Beet(2014) developed two models using a Bayesian approach which allowed for uncertainty in the sighting record by formally incorporating both certain and uncertain sightings, but in different ways. Interestingly, the two methods give completely different conclusions concerning the extinction of the Ivory-billed Woodpecker. We further examined these two methods to provide a mathematical explanation, and to explore in more depth, as to why the results differed from one another. It was found that the first model was more sensitive to the last uncertain sighting, while the second was more sensitive to the last certain sighting. The difficulties in choosing the appropriate model are discussed.

Multiannual forecasting of seasonal influenza dynamics reveals climatic and evolutionary drivers.

Human influenza occurs annually in most temperate climatic zones of the world, with epidemics peaking in the cold winter months. Considerable debate surrounds the relative role of epidemic dynamics, viral evolution, and climatic drivers in driving year-to-year variability of outbreaks. The ultimate test of understanding is prediction; however, existing influenza models rarely forecast beyond a single year at best. Here, we use a simple epidemiological model to reveal multiannual predictability based on high-quality influenza surveillance data for Israel; the model fit is corroborated by simple metapopulation comparisons within Israel. Successful forecasts are driven by temperature, humidity, antigenic drift, and immunity loss. Essentially, influenza dynamics are a balance between large perturbations following significant antigenic jumps, interspersed with nonlinear epidemic dynamics tuned by climatic forcing.

A discrete Markov metapopulation model for persistence and extinction of species.

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values.

Modeling the Impact of White-Plague Coral Disease in Climate Change Scenarios.

Coral reefs are in global decline, with coral diseases increasing both in prevalence and in space, a situation that is expected only to worsen as future thermal stressors increase. Through intense surveillance, we have collected a unique and highly resolved dataset from the coral reef of Eilat (Israel, Red Sea), that documents the spatiotemporal dynamics of a White Plague Disease (WPD) outbreak over the course of a full season. Based on modern statistical methodologies, we develop a novel spatial epidemiological model that uses a maximum-likelihood procedure to fit the data and assess the transmission pattern of WPD. We link the model to sea surface temperature (SST) and test the possible effect of increasing temperatures on disease dynamics. Our results reveal that the likelihood of a susceptible coral to become infected is governed both by SST and by its spatial location relative to nearby infected corals. The model shows that the magnitude of WPD epidemics strongly depends on demographic circumstances; under one extreme, when recruitment is free-space regulated and coral density remains relatively constant, even an increase of only 0.5°C in SST can cause epidemics to double in magnitude. In reality, however, the spatial nature of transmission can effectively protect the community, restricting the magnitude of annual epidemics. This is because the probability of susceptible corals to become infected is negatively associated with coral density. Based on our findings, we expect that infectious diseases having a significant spatial component, such as Red-Sea WPD, will never lead to a complete destruction of the coral community under increased thermal stress. However, this also implies that signs of recovery of local coral communities may be misleading; indicative more of spatial dynamics than true rehabilitation of these communities. In contrast to earlier generic models, our approach captures dynamics of WPD both in space and time, accounting for the highly seasonal nature of annual WPD outbreaks.

The effects of connectivity on metapopulation persistence: network symmetry and degree correlations.

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation's dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in-out degree distribution, namely the 'in-out degree correlation' (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in-out degree distribution and particularly, the IODC are dominant factors controlling persistence.

The stabilizing role of the Sabbath in pre-monarchic Israel: a mathematical model.

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the "Basic Sabbath Number ש0"-a critical observance of the Sabbath, or large enough ש0, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.

A novel method for estimating the number of species within a region.

Ecologists are often required to estimate the number of species in a region or designated area. A number of diversity indices are available for this purpose and are based on sampling the area using quadrats or other means, and estimating the total number of species from these samples. In this paper, a novel theory and method for estimating the number of species is developed. The theory involves the use of the Laplace method for approximating asymptotic integrals. The method is shown to be successful by testing random simulated datasets. In addition, several real survey datasets are tested, including forests that contain a large number (tens to hundreds) of tree species, and an aquatic system with a large number of fish species. The method is shown to give accurate results, and in almost all cases found to be superior to existing tools for estimating diversity.

A test for a shift in the boundary of the geographical range of a species.

One predicted impact of climate change is a poleward shift in the boundaries of species ranges. Existing methods for identifying such a boundary shift based on changes in the observed pattern of occupancy within a grid of cells are sensitive to changes in the overall rate of sightings and their latitudinal distribution that are unconnected to a boundary shift. A formal test for a boundary shift is described that allows for such changes. The test is applied to detect northward shifts in the northern boundary of the Essex skipper (Thymelicus lineola) butterfly and the European goldfinch (Carduelis carduelis) in Great Britain. A shift is detected in the latter case but not in the former. Results from a simulation study are presented showing that the test performs well.

Modelling the unexpected dynamics of COVID-19 in Manaus, Brazil.

In late March 2020, SARS-CoV-2 arrived in Manaus, Brazil, and rapidly developed into a large-scale epidemic that collapsed the local health system and resulted in extreme death rates. Several key studies reported that ∼76% of residents of Manaus were infected (attack rate AR≃76%) by October 2020, suggesting protective herd immunity had been reached. Despite this, an unexpected second wave of COVID-19 struck again in November and proved to be larger than the first, creating a catastrophe for the unprepared population. It has been suggested that this could be possible if the second wave was driven by reinfections. However, it is widely reported that reinfections were at a low rate (before the emergence of Omicron), and reinfections tend to be mild. Here, we use novel methods to model the epidemic from mortality data without considering reinfection-caused deaths and evaluate the impact of interventions to explain why the second wave appeared. The method fits a "flexible" reproductive number R0(t) that changes over the epidemic, and it is demonstrated that the method can successfully reconstruct R0(t) from simulated data. For Manaus, the method finds AR≃34% by October 2020 for the first wave, which is far less than required for herd immunity yet in-line with seroprevalence estimates. The work is complemented by a two-strain model. Using genomic data, the model estimates transmissibility of the new P.1 virus lineage as 1.9 times higher than that of the non-P.1. Moreover, an age class model variant that considers the high mortality rates of older adults show very similar results. These models thus provide a reasonable explanation for the two-wave dynamics in Manaus without the need to rely on large reinfection rates, which until now have only been found in negligible to moderate numbers in recent surveillance efforts.

Assessing the impact of Australia's mass vaccination campaigns over the Delta and Omicron outbreaks.

BACKGROUND: The Australian Government implemented a national vaccination campaign against COVID-19 beginning February 22, 2021. The roll-out was criticised for being delayed relative to many high-income countries, but high levels of vaccination coverage were belatedly achieved. The large-scale Omicron outbreak in January 2022 resulted in a massive number of cases and deaths, although mortality would have been far higher if not for vigorous efforts to rapidly vaccinate the entire population. The impact of the vaccination coverage was assessed over this extended period. METHODS: We considered NSW, as the Australian jurisdiction with the highest quality data for our purposes and which still reflected the national experience. Weekly death rates were derived among individuals aged 50+ with respect to vaccine status between August 8, 2021 and July 9, 2022. We evaluated deaths averted by the vaccination campaign by modelling alternative counterfactual scenarios based on a simple data-driven modelling methodology presented by Jia et al. (2023). FINDINGS: Unvaccinated individuals had a 7.7-fold greater mortality rate than those who were fully vaccinated among people aged 50+, which rose to 11.2-fold in those who had received a booster dose. If NSW had fully vaccinated its ~2.9 million 50+ residents earlier (by July 28, 2021), only 440 of the total 3,495 observed 50+ deaths would have been averted. Up to July 9, 2022, the booster campaign prevented 1,860 deaths. In the absence of a vaccination campaign, ~21,250 COVID-19 50+ deaths (conservative estimate) could have been expected in NSW i.e., some 6 times the actual total. We also find the methodology of Jia et al. (2023) can sometimes significantly underestimate that actual number. INTERPRETATION: The Australian vaccination campaign was successful in reducing mortality over 2022, relative to alternative hypothetical vaccination scenarios. The success was attributable to the Australian public's high levels of engagement with vaccination in the face of new SARS-COV-2 variants, and because high levels of vaccination coverage (full and booster) were achieved in the period shortly before the major Omicron outbreak of 2022.

Seasonal dynamics of recurrent epidemics.

Seasonality is a driving force that has a major effect on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases (such as influenza, measles, chickenpox and pertussis), and is of great relevance for host-parasite relationships in general. Here we gain further insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR (susceptible, infectious or recovered) epidemic model. Our analysis differs from other modelling studies in that the focus is more on post-epidemic dynamics than the outbreak itself. Despite the mathematical intractability of the forced SIR model, we identify a new threshold effect and give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak, or a 'skip'-a year in which an epidemic fails to initiate. The threshold is determined by the population's susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population. Moreover, the time of occurrence (that is, the phase) of an outbreak proves to be a useful parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-peaking diseases (that is, those having high phase) from spreading widely, thereby increasing population susceptibility, and controlling the triggering and intensity of future epidemics. These principles yield forecasting tools that should have relevance for the study of newly emerging and re-emerging diseases controlled by seasonal vectors.

Rapid global spread of variants of concern of SARS-CoV-2.

Objectives: Variants of concern (VOCs) of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), such as the Delta variant and the Omicron variant, have reached all countries/regions of the world and have had a tremendous impact. This study analyses the global spread of VOCs of SARS-CoV-2. Methods: Biweekly aggregated numbers of several VOCs were retrieved for 58 locations. The time interval for the proportion of VOC samples to exceed 60% (indicating dominance) among all samples sequenced in each location was calculated. The times taken for a VOC to become dominant in 12 (or 36) locations was defined in order to quantify the speed of spread. Results: It took 63, 56 and 28 days for the Alpha, Delta and Omicron variants to become dominant in 12 locations, respectively, and 133, 70 and 28 days for the Alpha, Delta and Omicron variants to become dominant in 36 locations. Conclusions: The Omicron variant has much higher transmission potential compared with the Delta variant, and the Delta variant has higher transmission potential compared with the pre-Delta VOCs.

Determinants of periodicity in seasonally driven epidemics.

Seasonality strongly affects the transmission and spatio-temporal dynamics of many infectious diseases, and is often an important cause for their recurrence. However, there are many open questions regarding the intricate relationship between seasonality and the complex dynamics of infectious diseases it gives rise to. For example, in the analysis of long-term time-series of childhood diseases, it is not clear why there are transitions from regimes with regular annual dynamics, to regimes in which epidemics occur every two or more years, and vice-versa. The classical seasonally-forced SIR epidemic model gives insights into these phenomena but due to its intrinsic nonlinearity and complex dynamics, the model is rarely amenable to detailed mathematical analysis. Making sensible approximations we analytically study the threshold (bifurcation) point of the forced SIR model where there is a switch from annual to biennial epidemics. We derive, for the first time, a simple equation that predicts the relationship between key epidemiological parameters near the bifurcation point. The relationship makes clear that, for realistic values of the parameters, the transition from biennial to annual dynamics will occur if either the birth-rate (µ) or basic reproductive ratio (R(0)) is increased sufficiently, or if the strength of seasonality (δ) is reduced sufficiently. These effects are confirmed in simulations studies and are also in accord with empirical observations. For example, the relationship may explain the correspondence between documented transitions in measles epidemics dynamics and concomitant changes in demographic and environmental factors.

Modelling the spread of diseases in clustered networks.

It is now well appreciated that population structure can have a major impact on disease dynamics, outbreak sizes and epidemic thresholds. Indeed, on some networks, epidemics occur only for sufficiently high transmissibility, whereas in others (e.g. scale-free networks), no such threshold effect exists. While the effects of variability in connectivity are relatively well known, the effects of clustering in the population on disease dynamics are still debated. We develop a simple and intuitive model for calculating the reproductive number R(0) on clustered networks with arbitrary degree distribution. The model clearly shows that in general, clustering impedes epidemic spread; however, its effects are usually small and/or coupled with other topological properties of the network. The model is generalized to take into account degree-dependent transmissibility (e.g., relevant for disease vectors). The model is also used to easily rederive a known result concerning the formation of the giant component.