Epidemic cycles driven by host behaviour

Rates of SARS-CoV-2 transmission and vaccination impact the fate of vaccine-resistant strains

Vaccines are thought to be the best available solution for controlling the ongoing SARS-CoV-2 pandemic. However, the emergence of vaccine-resistant strains may come too rapidly for current vaccine developments to alleviate the health, economic and social consequences of the pandemic. To quantify and characterize the risk of such a scenario, we created a SIR-derived model with initial stochastic dynamics of the vaccine-resistant strain to study the probability of its emergence and establishment. Using parameters realistically resembling SARS-CoV-2 transmission, we model a wave-like pattern of the pandemic and consider the impact of the rate of vaccination and the strength of non-pharmaceutical intervention measures on the probability of emergence of a resistant strain. As expected, we found that a fast rate of vaccination decreases the probability of emergence of a resistant strain. Counterintuitively, when a relaxation of non-pharmaceutical interventions happened at a time when most individuals of the population have already been vaccinated the probability of emergence of a resistant strain was greatly increased. Consequently, we show that a period of transmission reduction close to the end of the vaccination campaign can substantially reduce the probability of resistant strain establishment. Our results suggest that policymakers and individuals should consider maintaining non-pharmaceutical interventions and transmission-reducing behaviours throughout the entire vaccination period.

A review and agenda for integrated disease models including social and behavioural factors

Social and behavioural factors are critical to the emergence, spread and containment of human disease, and are key determinants of the course, duration and outcomes of disease outbreaks. Recent epidemics of Ebola in West Africa and coronavirus disease 2019 (COVID-19) globally have reinforced the importance of developing infectious disease models that better integrate social and behavioural dynamics and theories. Meanwhile, the growth in capacity, coordination and prioritization of social science research and of risk communication and community engagement (RCCE) practice within the current pandemic response provides an opportunity for collaboration among epidemiological modellers, social scientists and RCCE practitioners towards a mutually beneficial research and practice agenda. Here, we provide a review of the current modelling methodologies and describe the challenges and opportunities for integrating them with social science research and RCCE practice. Finally, we set out an agenda for advancing transdisciplinary collaboration for integrated disease modelling and for more robust policy and practice for reducing disease transmission.

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance between strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the “one disease equals one pathogen” paradigm.

Epidemics rarely involve a single unique pathogen but are often modelled as such. Rather, most pathogens circulate under a family of strains which can interact differently with the host immune system and undergo further mutations. Here we extend a classic epidemiological model to consider the genetic structure connecting these strains—i.e., the genotype network mapping possible mutation pathways—and investigate the dynamics and emergence of epidemics beyond the “one disease equals one pathogen” paradigm. This simple model allows us to consider the impacts of (i) mutation, (ii) cross-immunity between strains, (iii) competition between strains, and (iv) the structure of the genotype network. We find that, altogether, these features do not affect the classic epidemic threshold but localize outbreaks around key strains and yield a second immune invasion threshold below which the epidemics follow almost cyclical and chaos-like dynamics. Our results illustrate how little biological realism is needed to introduce key features of real epidemics in even the simplest disease models: epidemic cycles, unpredictability, and heterogeneous strain prevalence.

Adaptive social contact rates induce complex dynamics during epidemics

Epidemics may pose a significant dilemma for governments and individuals. The personal or public health consequences of inaction may be catastrophic; but the economic consequences of drastic response may likewise be catastrophic. In the face of these trade-offs, governments and individuals must therefore strike a balance between the economic and personal health costs of reducing social contacts and the public health costs of neglecting to do so. As risk of infection increases, potentially infectious contact between people is deliberately reduced either individually or by decree. This must be balanced against the social and economic costs of having fewer people in contact, and therefore active in the labor force or enrolled in school. Although the importance of adaptive social contact on epidemic outcomes has become increasingly recognized, the most important properties of coupled human-natural epidemic systems are still not well understood. We develop a theoretical model for adaptive, optimal control of the effective social contact rate using traditional epidemic modeling tools and a utility function with delayed information. This utility function trades off the population-wide contact rate with the expected cost and risk of increasing infections. Our analytical and computational analysis of this simple discrete-time deterministic strategic model reveals the existence of an endemic equilibrium, oscillatory dynamics around this equilibrium under some parametric conditions, and complex dynamic regimes that shift under small parameter perturbations. These results support the supposition that infectious disease dynamics under adaptive behavior change may have an indifference point, may produce oscillatory dynamics without other forcing, and constitute complex adaptive systems with associated dynamics. Implications for any epidemic in which adaptive behavior influences infectious disease dynamics include an expectation of fluctuations, for a considerable time, around a quasi-equilibrium that balances public health and economic priorities, that shows multiple peaks and surges in some scenarios, and that implies a high degree of uncertainty in mathematical projections.

Robustness of behaviorally induced oscillations in epidemic models under a low rate of imported cases

This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a nonoscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.

Dynamics of beneficial epidemics

Pathogens can spread epidemically through populations. Beneficial contagions, such as viruses that enhance host survival or technological innovations that improve quality of life, also have the potential to spread epidemically. How do the dynamics of beneficial biological and social epidemics differ from those of detrimental epidemics? We investigate this question using a breadth-first modeling approach involving three distinct theoretical models. First, in the context of population genetics, we show that a horizontally-transmissible element that increases fitness, such as viral DNA, spreads superexponentially through a population, more quickly than a beneficial mutation. Second, in the context of behavioral epidemiology, we show that infections that cause increased connectivity lead to superexponential fixation in the population. Third, in the context of dynamic social networks, we find that preferences for increased global infection accelerate spread and produce superexponential fixation, but preferences for local assortativity halt epidemics by disconnecting the infected from the susceptible. We conclude that the dynamics of beneficial biological and social epidemics are characterized by the rapid spread of beneficial elements, which is facilitated in biological systems by horizontal transmission and in social systems by active spreading behavior of infected individuals.

The calendar year fallacy: The danger of reliance on calendar year data in end-of-life capacity and financial planning

Planners, actuaries, and others involved in forecasting capacity and costs must manipulate historical data. Data from calendar/financial year totals have been assumed to be adequate and reliable. This relies on the assumption that year-to-year differences do not arise from patterns concealed in the data. While the seasonal cycle is widely recognized, longer term patterns such as disease outbreaks will act to modify annual demand and costs. Monthly data relating to deaths in local government areas in England and Wales are used to demonstrate curious semipermanent bursts of high behavior. There is no seasonal pattern for the start of these events, and the sudden switch to high deaths can occur at any time, even in immediately adjacent areas. Higher deaths and related demand and costs endure for around 12 months before they suddenly revert to the former level where they stay until the next of these curious high events. In England and Wales (and many other countries), a period of unexplained higher deaths, reduced life expectancy, and health care and life insurance costs since 2011 appears to be coming to an end and looks to have arisen from a coincidence of these events at sub-national level.

A stochastic SIR network epidemic model with preventive dropping of edges

A Markovian Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size [Formula: see text], assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy-Reed (in which the degrees of individuals are deterministic) and Newman-Strogatz-Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman-Strogatz-Watts version. The basic reproduction number [Formula: see text] and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when [Formula: see text], the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N.

Bursting endemic bubbles in an adaptive network

The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavioral change have found oscillations, but in an extremely narrow region of the parameter space, which contrasts with intuition and available data. In this paper we propose a simple susceptible-infected-susceptible epidemic model on an adaptive network with time-delayed rewiring, and show that oscillatory solutions are now present in a wide region of the parameter space. Altering the transmission or rewiring rates reveals the presence of an endemic bubble—an enclosed region of the parameter space where oscillations are observed.

European Neolithic societies showed early warning signals of population collapse

Ecosystems on the verge of major reorganization-regime shift-may exhibit declining resilience, which can be detected using a collection of generic statistical tests known as early warning signals (EWSs). This study explores whether EWSs anticipated human population collapse during the European Neolithic. It analyzes recent reconstructions of European Neolithic (8-4 kya) population trends that reveal regime shifts from a period of rapid growth following the introduction of agriculture to a period of instability and collapse. We find statistical support for EWSs in advance of population collapse. Seven of nine regional datasets exhibit increasing autocorrelation and variance leading up to collapse, suggesting that these societies began to recover from perturbation more slowly as resilience declined. We derive EWS statistics from a prehistoric population proxy based on summed archaeological radiocarbon date probability densities. We use simulation to validate our methods and show that sampling biases, atmospheric effects, radiocarbon calibration error, and taphonomic processes are unlikely to explain the observed EWS patterns. The implications of these results for understanding the dynamics of Neolithic ecosystems are discussed, and we present a general framework for analyzing societal regime shifts using EWS at large spatial and temporal scales. We suggest that our findings are consistent with an adaptive cycling model that highlights both the vulnerability and resilience of early European populations. We close by discussing the implications of the detection of EWS in human systems for archaeology and sustainability science.

Eradicating infectious disease using weakly transmissible vaccines

Viral vaccines have had remarkable positive impacts on human health as well as the health of domestic animal populations. Despite impressive vaccine successes, however, many infectious diseases cannot yet be efficiently controlled or eradicated through vaccination, often because it is impossible to vaccinate a sufficient proportion of the population. Recent advances in molecular biology suggest that the centuries-old method of individual-based vaccine delivery may be on the cusp of a major revolution. Specifically, genetic engineering brings to life the possibility of a live, transmissible vaccine. Unfortunately, releasing a highly transmissible vaccine poses substantial evolutionary risks, including reversion to high virulence as has been documented for the oral polio vaccine. An alternative, and far safer approach, is to rely on genetically engineered and weakly transmissible vaccines that have reduced scope for evolutionary reversion. Here, we use mathematical models to evaluate the potential efficacy of such weakly transmissible vaccines. Our results demonstrate that vaccines with even a modest ability to transmit can significantly lower the incidence of infectious disease and facilitate eradication efforts. Consequently, weakly transmissible vaccines could provide an important tool for controlling infectious disease in wild and domestic animal populations and for reducing the risks of emerging infectious disease in humans.

Asymmetric percolation drives a double transition in sexual contact networks

Zika virus (ZIKV) exhibits unique transmission dynamics in that it is concurrently spread by a mosquito vector and through sexual contact. Due to the highly asymmetric durations of infectiousness between males and females-it is estimated that males are infectious for periods up to 10 times longer than females-we show that this sexual component of ZIKV transmission behaves akin to an asymmetric percolation process on the network of sexual contacts. We exactly solve the properties of this asymmetric percolation on random sexual contact networks and show that this process exhibits two epidemic transitions corresponding to a core-periphery structure. This structure is not present in the underlying contact networks, which are not distinguishable from random networks, and emerges because of the asymmetric percolation. We provide an exact analytical description of this double transition and discuss the implications of our results in the context of ZIKV epidemics. Most importantly, our study suggests a bias in our current ZIKV surveillance, because the community most at risk is also one of the least likely to get tested.

Dynamics of epidemic diseases on a growing adaptive network

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

Behavioural change models for infectious disease transmission: a systematic review (2010-2015)

We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010-2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

Syphilis: Re-emergence of an old foe

Syphilis is caused by infection with Treponema pallidum subsp. pallidum, a not-yet-cultivable spiral-shaped bacterium that is usually transmitted by sexual contact with an infected partner or by an infected pregnant woman to her fetus. There is no vaccine to prevent syphilis. Diagnosis and treatment of infected individuals and their contacts is key to syphilis control programs that also include sex education and promotion of condom use to prevent infection. Untreated syphilis can progress through four stages: primary (chancre, regional lymphadenopathy), secondary (disseminated skin eruptions, generalized lymphadenopathy), latent (decreased re-occurrence of secondary stage manifestations, absence of symptoms), and tertiary (gummas, cardiovascular syphilis and late neurological symptoms). The primary and secondary stages are the most infectious. WHO estimates that each year 11 million new cases of syphilis occur globally among adults aged 15-49 years. Syphilis has re-emerged in several regions including North America, Western Europe, China and Australia. Host-associated factors that drive the re-emergence and spread of syphilis include high-risk sexual activity, migration and travel, and economic and social changes that limit access to health care. Early, uncomplicated syphilis is curable with a single intramuscular injection of benzathine penicillin G (BPG), the first line drug for all stages of syphilis. Emergence of macrolide-resistant T. pallidum has essentially precluded the empirical use of azithromycin as a second-line drug for treatment of syphilis. Virulence attributes of T. pallidum are poorly understood. Genomic and proteomic studies have provided some new information concerning how this spirochete may evade host defense mechanisms to persist for long periods in the host.

The determinant of periodicity in Mycoplasma pneumoniae incidence: an insight from mathematical modelling

Until the early 1990 s, incidences of Mycoplasma pneumoniae (MP) infection showed three to five year epidemic cycles in multiple countries, however, the mechanism for the MP epidemic cycle has not been understood. Here, we investigate the determinant of periodicity in MP incidence by employing a mathematical model describing MP transmission dynamics. Three candidates for the determinant of periodicity were evaluated: school-term forcing, minor variance in the duration of immunity, and epidemiological interference between MP serotypes. We find that minor variation in the duration of immunity at the population level must be considered essential for the MP epidemic cycle because the MP cyclic incidence pattern did not replicate without it. Minor variation, in this case, is a less dispersed distribution for the duration of immunity than an exponential distribution. Various lengths of epidemic cycles, including cycles typically found in nature, e.g. three to five year cycles, were also observed when there was minor variance in the duration of immunity. The cyclic incidence pattern is robust even if there is epidemiological interference due to cross-immune protection, which is observed in the epidemiological data as negative correlation between epidemics per MP serotype.

Syphilis in the economic center of South China: results from a real-time, web-based surveillance program

Background

Guangzhou is the economic center of South China, which is currently suffering an insidious re-emergence of syphilis. Syphilis epidemic in this area is a matter of serious concern, because of the special economic position of Guangzhou and its large migrant population. Therefore, a comprehensive analysis of surveillance data is needed to provide further information for developing targeted control programs.

Method

Case-based surveillance data obtained from a real-time, web-based system were analyzed. A hierarchical clustering method was applied to classify the 12 districts of Guangzhou into several epidemiological regions. The district-level annual incidence and clustering results were displayed on the same map to show the spatial patterns of syphilis in Guangzhou.

Results

A total of 60,178 syphilis cases were reported during the period from 2005 to 2013, among which primary/secondary syphilis accounted for 15,864 cases (26.36 %), latent syphilis for 41,078 cases (68.26 %) and congenital syphilis for 2,090 cases (3.47 %). Moreover, primary/secondary syphilis burden slightly decreased from 17.5-18.0 cases per 100,000 people in the first years to 10.6 cases per 100,000 in 2013, with latent syphilis largely increasing from 18.5 cases per 100,000 to 43.4 cases per 100,000. Districts of Guangzhou could be classified into 3 epidemiological regions according to the syphilis burden over the last 3 years of the study period.

Conclusions

The burden of primary/secondary syphilis appears to be decreasing in recent years, whereas that of latent syphilis is increasing. Given the epidemiological features and the annual changes found in this study, it is suggested that future control programs should be more population-specific and spatially targeted.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-015-1072-z) contains supplementary material, which is available to authorized users.

Asymptomatic transmission and the resurgence of Bordetella pertussis

BACKGROUND

The recent increase in whooping cough incidence (primarily caused by Bordetella pertussis) presents a challenge to both public health practitioners and scientists trying to understand the mechanisms behind its resurgence. Three main hypotheses have been proposed to explain the resurgence: 1) waning of protective immunity from vaccination or natural infection over time, 2) evolution of B. pertussis to escape protective immunity, and 3) low vaccine coverage. Recent studies have suggested a fourth mechanism: asymptomatic transmission from individuals vaccinated with the currently used acellular B. pertussis vaccines.

METHODS

Using wavelet analyses of B. pertussis incidence in the United States (US) and United Kingdom (UK) and a phylodynamic analysis of 36 clinical B. pertussis isolates from the US, we find evidence in support of asymptomatic transmission of B. pertussis. Next, we examine the clinical, public health, and epidemiological consequences of asymptomatic B. pertussis transmission using a mathematical model.

RESULTS

We find that: 1) the timing of changes in age-specific attack rates observed in the US and UK are consistent with asymptomatic transmission; 2) the phylodynamic analysis of the US sequences indicates more genetic diversity in the overall bacterial population than would be suggested by the observed number of infections, a pattern expected with asymptomatic transmission; 3) asymptomatic infections can bias assessments of vaccine efficacy based on observations of B. pertussis-free weeks; 4) asymptomatic transmission can account for the observed increase in B. pertussis incidence; and 5) vaccinating individuals in close contact with infants too young to receive the vaccine ("cocooning" unvaccinated children) may be ineffective.

CONCLUSIONS

Although a clear role for the previously suggested mechanisms still exists, asymptomatic transmission is the most parsimonious explanation for many of the observations surrounding the resurgence of B. pertussis in the US and UK. These results have important implications for B. pertussis vaccination policy and present a complicated scenario for achieving herd immunity and B. pertussis eradication.