Dynamics of infectious diseases

A deep-SIQRV epidemic model for COVID-19 to access the impact of prevention and control measures

The coronavirus (COVID-19) has mutated into several variants, and evidence says that new variants are more transmissible than existing variants. Even with full-scale vaccination efforts, the theoretical threshold for eradicating COVID-19 appears out of reach. This article proposes an artificial intelligence(AI) based intelligent prediction model called Deep-SIQRV(Susceptible-Infected-Quarantined-Recovered-Vaccinated) to simulate the spreading of COVID-19. While many models assume that vaccination provides lifetime protection, we focus on the impact of waning immunity caused by the conversion of vaccinated individuals back to susceptible ones. Unlike existing models, which assume that all coronavirus-infected individuals have the same infection rate, the proposed model considers the various infection rates to analyze transmission laws and trends. Next, we consider the influence of prevention and control strategies, such as media marketing and law enforcement, on the spread of the epidemic. We employed the PAN-LDA model to extract features from COVID-19-related discussions on social media and online news articles. Moreover, the Long Short Term Memory(LSTM) model and Evolution Strategies(ES) are used to optimize transmission rates of infection and other model parameters, respectively. The experimental results on epidemic data from various Indian states demonstrate that persons infected with coronavirus had a more significant infection rate within four to nine days after infection, which corresponds to the actual transmission laws of the epidemic. The experimental results show that the proposed model has good prediction ability and obtains the Mean Absolute Percentage Error(MAPE) of 0.875%, 0.965%, 0.298%, and 0.215% for the next eight days in Maharashtra, Kerala, Karnataka, and Delhi, respectively. Our findings highlight the significance of using vaccination data, COVID-19-related posts, and information generated by the government's tremendous efforts in the prediction calculation process.

Age-related model for estimating the symptomatic and asymptomatic transmissibility of COVID-19 patients

Estimation of age-dependent transmissibility of COVID-19 patients is critical for effective policymaking. Although the transmissibility of symptomatic cases has been extensively studied, asymptomatic infection is understudied due to limited data. Using a dataset with reliably distinguished symptomatic and asymptomatic statuses of COVID-19 cases, we propose an ordinary differential equation model that considers age-dependent transmissibility in transmission dynamics. Under a Bayesian framework, multi-source information is synthesized in our model for identifying transmissibility. A shrinkage prior among age groups is also adopted to improve the estimation behavior of transmissibility from age-structured data. The added values of accounting for age-dependent transmissibility are further evaluated through simulation studies. In real-data analysis, we compare our approach with two basic models using the deviance information criterion (DIC) and its extension. We find that the proposed model is more flexible for our epidemic data. Our results also suggest that the transmissibility of asymptomatic infections is significantly lower (on average, 76.45% with a credible interval (27.38%, 88.65%)) than that of symptomatic cases. In both symptomatic and asymptomatic patients, the transmissibility mainly increases with age. Patients older than 30 years are more likely to develop symptoms with higher transmissibility. We also find that the transmission burden of asymptomatic cases is lower than that of symptomatic patients.

A Sequential Cross-Sectional Analysis Producing Robust Weekly COVID-19 Rates for South East Asian Countries

The COVID-19 pandemic has expanded fast over the world, affecting millions of people and generating serious health, social, and economic consequences. All South East Asian countries have experienced the pandemic, with various degrees of intensity and response. As the pandemic progresses, it is important to track and analyse disease trends and patterns to guide public health policy and treatments. In this paper, we carry out a sequential cross-sectional study to produce reliable weekly COVID-19 death (out of cases) rates for South East Asian countries for the calendar years 2020, 2021, and 2022. The main objectives of this study are to characterise the trends and patterns of COVID-19 death rates in South East Asian countries through time, as well as compare COVID-19 rates among countries and regions in South East Asia. Our raw data are (daily) case and death counts acquired from "Our World in Data", which, however, for some countries and time periods, suffer from sparsity (zero or small counts), and therefore require a modelling approach where information is adaptively borrowed from the overall dataset where required. Therefore, a sequential cross-sectional design will be utilised, that will involve examining the data week by week, across all countries. Methodologically, this is achieved through a two-stage random effect shrinkage approach, with estimation facilitated by nonparametric maximum likelihood.

On the Convexity of the Effective Reproduction Number

In this study, we analyze the evolution of the effective reproduction number, R, through a Susceptible-Infective-Recovered spreading process in heterogeneous populations; Characterizing its decay process allows to analytically study the effects of countermeasures on the progress of the virus under heterogeneity, and to optimize their policies. A striking result of recent studies has shown that heterogeneity across individuals (or superspreading) may have a drastic effect on the spreading process progression, which may cause a nonlinear decrease of R in the number of infected individuals. We account for heterogeneity and analyze the stochastic progression of the spreading process. We show that the decrease of R is, in fact, convex in the number of infected individuals, where this convexity stems from heterogeneity. The analysis is based on establishing stochastic monotonic relations between the susceptible populations in varying times of the spread. We demonstrate that the convex behavior of the effective reproduction number affects the performance of countermeasures used to fight the spread of a virus. The results are applicable to the control of virus and malware spreading in computer networks as well. We examine numerically the sensitivity of the herd immunity threshold to the heterogeneity level and to the chosen countermeasures policy.

A Statistical Synopsis of COVID-19 Components and Descriptive Analysis of Their Socio-Economic and Healthcare Aspects in Bangladesh Perspective

The aim of the work is to analyze the socio-economic and healthcare aspects that arise in the contemporary COVID-19 situation from Bangladesh perspective. We elaborately discuss the successive COVID-19 occurrences in Bangladesh with consequential information. The components associated with the COVID-19 commencement and treatment policy with corresponding features and their consequences are patently delineated. The effect of troublesome issues related to the treatment is detailed with supporting real-time data. We elucidate the applications of modern technologies advancement in epidemiological aspects and their existent compatibility in Bangladesh. We statistically analyze the real-time data through figurative and tabular approaches. Some relevant measures of central tendency and dispersion are utilized to explore the data structure and its observable specifications. For a clear manifestation, Z- scores of the COVID-19 components are analyzed through the Box-Whisker plot. We have discovered that the gathered data exhibit features that are unsatisfactory for the normal distribution, are highly positively skewed, and are predominated by the earliest occurrences. Infections and deaths were initially lower than the global average, but they drastically rose in the first quarter of 2021 and persisted for the remainder of the year. Substantial preventive results were produced by the region-wisetime-worthy moves. In the fourth quarter of 2021, the infections and deaths noticeably decreased, and the number of recoveries was highly significant. In the middle of 2022, a lethal rise in infections was observed in Bangladesh and that was quickly stabilized, and the pandemic ingredients were under control. According to our assessment, some concluding remarks are made at the end of this work.

The stochastic world of emerging viruses

The acquisition of new hosts is a fundamental mechanism by which parasitic organisms expand their host range and perpetuate themselves on an evolutionary scale. Among pathogens, viruses, due to their speed of evolution, are particularly efficient in producing new emergence events. However, even though these phenomena are particularly important to the human species and therefore specifically studied, the processes of virus emergence in a new host species are very complex and difficult to comprehend in their entirety. In order to provide a structured framework for understanding emergence in a species (including humans), a comprehensive qualitative model is an indispensable cornerstone. This model explicitly describes all the stages necessary for a virus circulating in the wild to come to the crossing of the epidemic threshold. We have therefore developed a complete descriptive model explaining all the steps necessary for a virus circulating in host populations to emerge in a new species. This description of the parameters presiding over the emergence of a new virus allows us to understand their nature and importance in the emergence process.

Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading

The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop.

Mobile human ad hoc networks: A communication engineering viewpoint on interhuman airborne pathogen transmission

A number of transmission models for airborne pathogens transmission, as required to understand airborne infectious diseases such as COVID-19, have been proposed independently from each other, at different scales, and by researchers from various disciplines. We propose a communication engineering approach that blends different disciplines such as epidemiology, biology, medicine, and fluid dynamics. The aim is to present a unified framework using communication engineering, and to highlight future research directions for modeling the spread of infectious diseases through airborne transmission. We introduce the concept of mobile human ad hoc networks (MoHANETs), which exploits the similarity of airborne transmission-driven human groups with mobile ad hoc networks and uses molecular communication as the enabling paradigm. In the MoHANET architecture, a layered structure is employed where the infectious human emitting pathogen-laden droplets and the exposed human to these droplets are considered as the transmitter and receiver, respectively. Our proof-of-concept results, which we validated using empirical COVID-19 data, clearly demonstrate the ability of our MoHANET architecture to predict the dynamics of infectious diseases by considering the propagation of pathogen-laden droplets, their reception and mobility of humans.

Revisiting the standard for modeling the spread of infectious diseases

The COVID-19 epidemic brought to the forefront the value of mathematical modelling for infectious diseases as a guide to help manage a formidable challenge for human health. A standard dynamic model widely used for a spreading epidemic separates a population into compartments-each comprising individuals at a similar stage before, during, or after infection-and keeps track of the population fraction in each compartment over time, by balancing compartment loading, discharge, and accumulation rates. The standard model provides valuable insight into when an epidemic spreads or what fraction of a population will have been infected by the epidemic's end. A subtle issue, however, with that model, is that it may misrepresent the peak of the infectious fraction of a population, the time to reach that peak, or the rate at which an epidemic spreads. This may compromise the model's usability for tasks such as "Flattening the Curve" or other interventions for epidemic management. Here we develop an extension of the standard model's structure, which retains the simplicity and insights of the standard model while avoiding the misrepresentation issues mentioned above. The proposed model relies on replacing a module of the standard model by a module resulting from Padé approximation in the Laplace domain. The Padé-approximation module would also be suitable for incorporation in the wide array of standard model variants used in epidemiology. This warrants a re-examination of the subject and could potentially impact model-based management of epidemics, development of software tools for practicing epidemiologists, and related educational resources.

Characterizing stages of COVID-19 epidemics: a nonlinear physics perspective based on amplitude equations

The relevant dynamics underlying COVID-19 waves is described from an amplitude space perspective. To this end, the amplitude dynamics of infected populations is considered in different stages of epidemic waves. Eigenvectors and their corresponding amplitudes are derived analytically for low-dimensional models and by means of computational methods for high-dimensional models. It is shown that the amplitudes of all eigenvectors as functions of time can be tracked through the diverse stages of COVID-19 waves featuring jumps at the stage boundaries. In particular, it is shown that under certain circumstances the initial, outbreak stage and the final, subsiding stage of an epidemic wave are primarily determined by the unstable eigenvector of the initial stage and its corresponding remnant vector of the final stage. The corresponding amplitude captures most of the dynamics of the emerging and subsiding epidemics such that the problem at hand effectively becomes one dimensional leading to a dramatic reduction of the complexity of the problem at hand. Explicitly demonstrated for the first-wave COVID-19 epidemics of the year 2020 in the state of New York and Pakistan are given.

Digital twins based on bidirectional LSTM and GAN for modelling the COVID-19 pandemic

The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in machine learning techniques have given rise to neural networks with the ability to learn and predict complex dynamics at reduced computational costs. Here we introduce two digital twins of a SEIRS model applied to an idealised town. The SEIRS model has been modified to take account of spatial variation and, where possible, the model parameters are based on official virus spreading data from the UK. We compare predictions from one digital twin based on a data-corrected Bidirectional Long Short-Term Memory network with predictions from another digital twin based on a predictive Generative Adversarial Network. The predictions given by these two frameworks are accurate when compared to the original SEIRS model data. Additionally, these frameworks are data-agnostic and could be applied to towns, idealised or real, in the UK or in other countries. Also, more compartments could be included in the SEIRS model, in order to study more realistic epidemiological behaviour.

COVID-19 Belgium: Extended SEIR-QD model with nursing homes and long-term scenarios-based forecasts

Following the spread of the COVID-19 pandemic and pending the establishment of vaccination campaigns, several non pharmaceutical interventions such as partial and full lockdown, quarantine and measures of physical distancing have been imposed in order to reduce the spread of the disease and to lift the pressure on healthcare system. Mathematical models are important tools for estimating the impact of these interventions, for monitoring the current evolution of the epidemic at a national level and for estimating the potential long-term consequences of relaxation of measures. In this paper, we model the evolution of the COVID-19 epidemic in Belgium with a deterministic age-structured extended compartmental model. Our model takes special consideration for nursing homes which are modelled as separate entities from the general population in order to capture the specific delay and dynamics within these entities. The model integrates social contact data and is fitted on hospitalisations data (admission and discharge), on the daily number of COVID-19 deaths (with a distinction between general population and nursing home related deaths) and results from serological studies, with a sensitivity analysis based on a Bayesian approach. We present the situation as in November 2020 with the estimation of some characteristics of the COVID-19 deduced from the model. We also present several mid-term and long-term projections based on scenarios of reinforcement or relaxation of social contacts for different general sectors, with a lot of uncertainties remaining.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

Vaccination against COVID-19 and society's return to normality in England: a modelling study of impacts of different types of naturally acquired and vaccine-induced immunity

OBJECTIVES

To project impacts of mass vaccination against COVID-19, and investigate possible impacts of different types of naturally acquired and vaccine-induced immunity on future dynamics of SARS-CoV-2 transmission from 2021 to 2024 in England.

DESIGN

Deterministic, compartmental, discrete-time Susceptible-Exposed-Infectious-Recovered (SEIR) modelling.

PARTICIPANTS

Population in England.

INTERVENTIONS

Mass vaccination programmes.

OUTCOME MEASURES

Daily and cumulative number of deaths from COVID-19.

RESULTS

If vaccine efficacy remains high (85%), the vaccine-induced sterilising immunity lasts ≥182 days, and the reinfectivity is greatly reduced (by ≥60%), annual mass vaccination programmes can prevent further COVID-19 outbreaks in England. Under optimistic scenarios, with annual revaccination programmes, the cumulative number of COVID-19 deaths is estimated to be from 130 000 to 150 000 by the end of 2024. However, the total number of COVID-19 deaths may be up to 431 000 by the end of 2024, under scenarios with compromised vaccine efficacy (62.5%), short duration of natural and vaccine immunity (365/182 days) and small reduction in reinfectivity (30%). Under the assumed scenarios, more frequent revaccinations are associated with smaller total numbers and lower peaks of daily deaths from COVID-19.

CONCLUSIONS

Under optimistic scenarios, mass immunisation using efficacious vaccines may enable society safely to return to normality. However, under plausible scenarios with low vaccine efficacy and short durability of immunity, COVID-19 could continue to cause recurrent waves of severe morbidity and mortality despite frequent vaccinations. It is crucial to monitor the vaccination effects in the real world, and to better understand characteristics of naturally acquired and vaccine-induced immunity against SARS-CoV-2.

Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases, i.e. the number of new infections generated by an infectious individual, is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the distribution of the number of secondary cases is skewed and often modeled using a negative binomial distribution. However, this may not always be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the mean and variance of this distribution when the data generating distribution is different from the one used for inference. We also analyze COVID-19 data from Hong Kong, India, and Rwanda, and quantify the proportion of cases responsible for 80% of transmission, [Formula: see text], while acknowledging the variation arising from the assumed offspring distribution. In a simulation study, we find that variance estimates may be biased when there is a substantial amount of heterogeneity, and that selection of the most accurate distribution from a set of distributions is important. In addition we find that the number of secondary cases for two of the three COVID-19 datasets is better described by a Poisson-lognormal distribution.

Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.

SEIR order parameters and eigenvectors of the three stages of completed COVID-19 epidemics: with an illustration for Thailand January to May 2020

By end of October 2020, the COVID-19 pandemic has taken a tragic toll of 1150 000 lives and this number is expected to increase. Despite the pandemic is raging in most parts of the world, in a few countries COVID-19 epidemics subsided due to successful implementations of intervention measures. A unifying perspective of the beginnings, middle stages, and endings of such completed COVID-19 epidemics is developed based on the order parameter and eigenvalue concepts of nonlinear physics, in general, and synergetics, in particular. To this end, a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model is used. It is shown that COVID-19 epidemic outbreaks follow a suitably defined SEIR order parameter. Intervention measures switch the eigenvalue of the order parameter from a positive to a negative value, and in doing so, stabilize the COVID-19 disease-free state. The subsiding of COVID-19 epidemics eventually follows the remnant of the order parameter of the infection dynamical system. These considerations are illustrated for the COVID-19 epidemic in Thailand from January to May 2020. The decay of effective contact rates throughout the three epidemic stages is demonstrated. Evidence for the sign-switching of the dominant eigenvalue is given and the order parameter and its stage-3 remnant are identified. The presumed impacts of interventions measures implemented in Thailand are discussed in this context.

Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number [Formula: see text] on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life face-to-face contact networks. These results suggest that the hardest hit areas, such as New York City, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

SARS-COV-2: SIR Model Limitations and Predictive Constraints

Background: The main purpose of this research is to describe the mathematical asymmetric patterns of susceptible, infectious, or recovered (SIR) model equation application in the light of coronavirus disease 2019 (COVID-19) skewness patterns worldwide. Methods: The research modeled severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) spreading and dissemination patterns sensitivity by redesigning time series data extraction of daily new cases in terms of deviation consistency concerning variables that sustain COVID-19 transmission. The approach opened a new scenario where seasonality forcing behavior was introduced to understand SARS-COV-2 non-linear dynamics due to heterogeneity and confounding epidemics scenarios. Results: The main research results are the elucidation of three birth- and death-forced seasonality persistence phases that can explain COVID-19 skew patterns worldwide. They are presented in the following order: (1) the environmental variables (Earth seasons and atmospheric conditions); (2) health policies and adult learning education (HPALE) interventions; (3) urban spaces (local indoor and outdoor spaces for transit and social-cultural interactions, public or private, with natural physical features (river, lake, terrain). Conclusions: Three forced seasonality phases (positive to negative skew) phases were pointed out as a theoretical framework to explain uncertainty found in the predictive SIR model equations that might diverge in outcomes expected to express the disease’s behaviour.

The value of infectious disease modeling and trend assessment: a public health perspective

INTRODUCTION

Disease outbreaks of acquired immunodeficiency syndrome, severe acute respiratory syndrome, pandemic H1N1, H7N9, H5N1, Ebola, Zika, Middle East respiratory syndrome, and recently COVID-19 have raised the attention of the public over the past half-century. Revealing the characteristics and epidemic trends are important parts of disease control. The biological scenarios including transmission characteristics can be constructed and translated into mathematical models, which can help to predict and gain a deeper understanding of diseases.

AREAS COVERED

This review discusses the models for infectious diseases and highlights their values in the field of public health. This information will be of interest to mathematicians and clinicians, and make a significant contribution toward the development of more specific and effective models. Literature searches were performed using the online database of PubMed (inception to August 2020).

EXPERT OPINION

Modeling could contribute to infectious disease control by means of predicting the scales of disease epidemics, indicating the characteristics of disease transmission, evaluating the effectiveness of interventions or policies, and warning or forecasting during the pre-outbreak of diseases. With the development of theories and the ability of calculations, infectious disease modeling would play a much more important role in disease prevention and control of public health.

Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

Estimating the herd immunity threshold by accounting for the hidden asymptomatics using a COVID-19 specific model

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lock-down and resulting spatial migration of population due to announcement of lock-down. A method is presented for estimating the model parameters from real-world data, and it is shown that the various phases in the observed epidemiological data are captured well. It is shown that increase of infections slows down and herd immunity is achieved when active symptomatic patients are 10-25% of the population for the four countries we studied. Finally, a method for estimating the number of asymptomatic patients, who have been the key hidden link in the spread of the infections, is presented.

Cost-effectiveness of Interventions to Increase HPV Vaccine Uptake

OBJECTIVES

We sought to prioritize interventions for increasing human papillomavirus (HPV) vaccination coverage based on cost-effectiveness from a US state perspective to inform decisions by policy makers.

METHODS

We developed a dynamic simulation model of HPV transmission and progression scaled to a medium-sized US state (5 million individuals). We modeled outcomes over 50 years comparing no intervention to a one-year implementation of centralized reminder and recall for HPV vaccination, school-located HPV vaccination, or quality improvement (QI) visits to primary care clinics. We used probabilistic sensitivity analysis to assess a range of plausible outcomes associated with each intervention. Cost-effectiveness was evaluated relative to a conservative willingness-to-pay threshold; $50 000 per quality-adjusted life-year (QALY) .

RESULTS

All interventions were cost-effective, relative to no intervention. QI visits had the lowest cost and cost per QALY gained ($1538 versus no intervention). Statewide implementation of centralized reminder and recall cost $28 289 per QALY gained versus QI visits. School-located vaccination had the highest cost but was cost-effective at $18 337 per QALY gained versus QI visits. Scaling to the US population, interventions could avert 3000 to 14 000 future HPV cancers. When varying intervention cost and impact over feasible ranges, interventions were typically preferred to no intervention, but cost-effectiveness varied between intervention strategies.

CONCLUSIONS

Three interventions for increasing HPV vaccine coverage were cost-effective and offered substantial health benefits. Policy makers seeking to increase HPV vaccination should, at minimum, dedicate additional funding for QI visits, which are consistently effective at low cost and may additionally consider more resource-intensive interventions (reminder and recall or school-located vaccination).

Quantifying superspreading for COVID-19 using Poisson mixture distributions

The number of secondary cases is an important parameter for the control of infectious diseases. When individual variation in disease transmission is present, like for COVID-19, the number of secondary cases is often modelled using a negative binomial distribution. However, this may not be the best distribution to describe the underlying transmission process. We propose the use of three other offspring distributions to quantify heterogeneity in transmission, and we assess the possible bias in estimates of the offspring mean and its overdispersion when the data generating distribution is different from the one used for inference. We find that overdispersion estimates may be biased when there is a substantial amount of heterogeneity, and that the use of other distributions besides the negative binomial should be considered. We revisit three previously analysed COVID-19 datasets and quantify the proportion of cases responsible for 80% of transmission, p 80% , while acknowledging the variation arising from the assumed offspring distribution. We find that the number of secondary cases for these datasets is better described by a Poisson-lognormal distribution.

Understanding contagion dynamics through microscopic processes in active Brownian particles

Together with the universally recognized SIR model, several approaches have been employed to understand the contagion dynamics of interacting particles. Here, Active Brownian particles (ABP) are introduced to model the contagion dynamics of living agents that perform a horizontal transmission of an infectious disease in space and time. By performing an ensemble average description of the ABP simulations, we statistically describe susceptible, infected, and recovered groups in terms of particle densities, activity, contagious rates, and random recovery times. Our results show that ABP reproduces the time dependence observed in traditional compartmental models such as the Susceptible-Infected-Recovery (SIR) models and allows us to explore the critical densities and the contagious radius that facilitates the virus spread. Furthermore, we derive a first-principles analytical expression for the contagion rate in terms of microscopic parameters, without considering free parameters as the classical SIR-based models. This approach offers a novel alternative to incorporate microscopic processes into analyzing SIR-based models with applications in a wide range of biological systems.

Controlling the Outbreak of COVID-19: A Noncooperative Game Perspective

COVID-19 is a global epidemic. Till now, there is no remedy for this epidemic. However, isolation and social distancing are seemed to be effective preventive measures to control this pandemic. Therefore, in this article, an optimization problem is formulated that accommodates both isolation and social distancing features of the individuals. To promote social distancing, we solve the formulated problem by applying a noncooperative game that can provide an incentive for maintaining social distancing to prevent the spread of COVID-19. Furthermore, the sustainability of the lockdown policy is interpreted with the help of our proposed game-theoretic incentive model for maintaining social distancing where there exists a Nash equilibrium. Finally, we perform an extensive numerical analysis that shows the effectiveness of the proposed approach in terms of achieving the desired social-distancing to prevent the outbreak of the COVID-19 in a noncooperative environment. Numerical results show that the individual incentive increases more than 85% with an increasing percentage of home isolation from 25% to 100% for all considered scenarios. The numerical results also demonstrate that in a particular percentage of home isolation, the individual incentive decreases with an increasing number of individuals.

COVID-19 interventions in some European countries induced bifurcations stabilizing low death states against high death states: An eigenvalue analysis based on the order parameter concept of synergetics

Taking a dynamical systems perspective, COVID-19 infections are assumed to spread out in a human population via an instability. Conversely, government interventions to reduce the spread of the disease and the number of fatalities may induce a bifurcation that stabilizes a desirable state with low numbers of COVID-19 cases and associated deaths. The key characteristic feature of an infection dynamical system in this context is the eigenvalue that determines the stability of the states under consideration and is known in synergetics as the order parameter eigenvalue. Using a SEIR-like infection disease model, the relevant order parameter and its eigenvalue are determined. A three stage methodology is proposed to track and estimate the eigenvalue through time. The method is applied to COVID-19 infection data reported from 20 European countries during the period of January 1, 2020 to June 15. It is shown that in 15 out of the 20 countries the eigenvalue switched its sign suggesting that during the reporting period an intervention bifurcation took place that stabilized the desirable low death state. It is shown that the eigenvalue analysis also allows for a ranking of countries by the degree of the stability of the infection-free state. For the investigated countries, Ireland was found to exhibit the most stable infection-free state. Finally, a six point classification scheme is suggested with groups 5 and 6 including countries that failed to stabilize the desirable infection-free low death state. In doing so, tools for assessing the effectiveness of government interventions are provided that are at the heart of bifurcation theory, in general, and synergetics, in particular.

The Epidemiological Framework for Biological Invasions (EFBI): an interdisciplinary foundation for the assessment of biosecurity threats

Emerging microparasite (e.g. viruses, bacteria, protozoa and fungi) epidemics and the introduction of non-native pests and weeds are major biosecurity threats worldwide. The likelihood of these threats is often estimated from probabilities of their entry, establishment, spread and ease of prevention. If ecosystems are considered equivalent to hosts, then compartment disease models should provide a useful framework for understanding the processes that underpin non-native species invasions. To enable greater cross-fertilisation between these two disciplines, the Epidemiological Framework for Biological Invasions (EFBI) is developed that classifies ecosystems in relation to their invasion status: Susceptible, Exposed, Infectious and Resistant. These states are linked by transitions relating to transmission, latency and recovery. This viewpoint differs markedly from the species-centric approaches often applied to non-native species. It allows generalisations from epidemiology, such as the force of infection, the basic reproductive ratio R0, super-spreaders, herd immunity, cordon sanitaire and ring vaccination, to be discussed in the novel context of non-native species and helps identify important gaps in the study of biological invasions. The EFBI approach highlights several limitations inherent in current approaches to the study of biological invasions including: (i) the variance in non-native abundance across ecosystems is rarely reported; (ii) field data rarely (if ever) distinguish source from sink ecosystems; (iii) estimates of the susceptibility of ecosystems to invasion seldom account for differences in exposure to non-native species; and (iv) assessments of ecosystem susceptibility often confuse the processes that underpin patterns of spread within -and between- ecosystems. Using the invasion of lakes as a model, the EFBI approach is shown to present a new biosecurity perspective that takes account of ecosystem status and complements demographic models to deliver clearer insights into the dynamics of biological invasions at the landscape scale. It will help to identify whether management of the susceptibility of ecosystems, of the number of vectors, or of the diversity of pathways (for movement between ecosystems) is the best way of limiting or reversing the population growth of a non-native species. The framework can be adapted to incorporate increasing levels of complexity and realism and to provide insights into how to monitor, map and manage biological invasions more effectively.

COVID-19 ORDER PARAMETERS AND ORDER PARAMETER TIME CONSTANTS OF ITALY AND CHINA: A MODELING APPROACH BASED ON SYNERGETICS

From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations. Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation. Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios. However, little is known about the relevant order parameters (synergetics) of COVID-19 bifurcations and the corresponding time constants. Those order parameters describe directions in compartment model spaces in which infection dynamics initially evolves. The corresponding time constants describe the speed of the dynamics along those directions. COVID-19 order parameters and their time constants are derived within a standard SEIR dynamical systems framework and determined explicitly for two published studies on COVID-19 trajectories in Italy and China. The results suggest the existence of certain relationships between order parameters, time constants, and reproduction ratios. However, the examples from Italy and China also suggest that COVID-19 order parameters and time constants in general depend on regional differences and the stage of the local COVID-19 epidemic under consideration. These findings may help to improve the forecasting of COVID-19 outbreaks in new hotspots around the world.

Reducing respiratory syncytial virus (RSV) hospitalization in a lower-income country by vaccinating mothers-to-be and their households

Respiratory syncytial virus is the leading cause of lower respiratory tract infection among infants. RSV is a priority for vaccine development. In this study, we investigate the potential effectiveness of a two-vaccine strategy aimed at mothers-to-be, thereby boosting maternally acquired antibodies of infants, and their household cohabitants, further cocooning infants against infection. We use a dynamic RSV transmission model which captures transmission both within households and communities, adapted to the changing demographics and RSV seasonality of a low-income country. Model parameters were inferred from past RSV hospitalisations, and forecasts made over a 10-year horizon. We find that a 50% reduction in RSV hospitalisations is possible if the maternal vaccine effectiveness can achieve 75 days of additional protection for newborns combined with a 75% coverage of their birth household co-inhabitants (~7.5% population coverage).

Dynamical analysis and control strategies of an SIVS epidemic model with imperfect vaccination on scale-free networks

Vaccination is an effective method to prevent the spread of infectious diseases. In this paper, we develop an SIVS epidemic model with degree-related transmission rates and imperfect vaccination on scale-free networks. Firstly, we derive two threshold parameters and existence conditions of multiple endemic equilibria. Secondly, not only the global asymptotical stability of disease-free equilibrium and the persistence of the disease are derived, but also the global attractivity of the unique endemic equilibrium is proved using the monotone iterative technique. Thirdly, the effects of various immunization schemes including uniform immunization, targeted immunization and acquaintance immunization are studied, and the optimal vaccination strategy is analyzed by Pontryagin's maximum principle. Finally, we perform numerical simulations to verify these theoretical results.

A Population Dynamics Model of Mosquito-Borne Disease Transmission, Focusing on Mosquitoes' Biased Distribution and Mosquito Repellent Use

We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the model clearly shows the existence of thresholds for mosquito repellent efficacy and its utilization rate in the human population with respect to the elimination of mosquito-borne diseases. Further, the results imply that the suppression of mosquito-borne diseases becomes more difficult when the mosquitoes' distribution is biased to a greater extent around the human population.

Studies on patients establish Crohn's disease as a manifestation of impaired innate immunity

The fruitless search for the cause of Crohn's disease has been conducted for more than a century. Various theories, including autoimmunity, mycobacterial infection and aberrant response to food and other ingested materials, have been abandoned for lack of robust proof. This review will provide the evidence, obtained from patients with this condition, that the common predisposition to Crohn's is a failure of the acute inflammatory response to tissue damage. This acute inflammation normally attracts large numbers of neutrophil leucocytes which engulf and clear bacteria and autologous debris from the inflamed site. The underlying predisposition in Crohn's disease is unmasked by damage to the bowel mucosa, predominantly through infection, which allows faecal bowel contents access to the vulnerable tissues within. Consequent upon failure of the clearance of these infectious and antigenic intestinal contents, it becomes contained, leading to a chronic granulomatous inflammation, producing cytokine release, local tissue damage and systemic symptoms. Multiple molecular pathologies extending across the whole spectrum of the acute inflammatory and innate immune response lead to the common predisposition in which defective monocyte and macrophage function plays a central role. Family linkage and exome sequencing together with GWAS have identified some of the molecules involved, including receptors, molecules involved in vesicle trafficking, and effector cells. Current therapy is immunosuppressant, which controls the symptoms but accentuates the underlying problem, which can only logically be tackled by correcting the primary lesion/s by gene therapy or genome editing, or through the development of drugs that stimulate innate immunity.

Complex System Approaches for Animal Health Surveillance

Many new and highly variable data are currently being produced by the many participants in farmed animal productions systems. These data hold the promise of new information with potential value for animal health surveillance. The current analytical paradigm for dealing with these new data is to implement syndromic surveillance systems, which focus mainly on univariate event detection methods applied to individual time series, with the goal of identifying epidemics in the population. This approach is relatively limited in the scope and not well-suited for extracting much of the additional information that is contained within these data. These approaches have value and should not be abandoned. However, an additional, new analytical paradigm will be needed if surveillance and disease control agencies wish to extract additional information from these data. We propose a more holistic analytical approach borrowed from complex system science that considers animal disease to be a product of the complex interactions between the many individuals, organizations and other factors that are involved in, or influence food production systems. We will discuss the characteristics of farmed animal food production systems that make them complex adaptive systems and propose practical applications of methods borrowed from complex system science to help animal health surveillance practitioners extract additional information from these new data.

Human rhinovirus spatial-temporal epidemiology in rural coastal Kenya, 2015-2016, observed through outpatient surveillance

Background: Human rhinovirus (HRV) is the predominant cause of upper respiratory tract infections, resulting in a significant public health burden. The virus circulates as many different types (168), each generating strong homologous, but weak heterotypic, immunity. The influence of these features on transmission patterns of HRV in the community is understudied. Methods: Nasopharyngeal swabs were collected from patients with symptoms of acute respiratory infection (ARI) at nine out-patient facilities across a Health and Demographic Surveillance System between December 2015 and November 2016. HRV was diagnosed by real-time RT-PCR, and the VP4/VP2 genomic region of the positive samples sequenced. Phylogenetic analysis was used to determine the HRV types. Classification models and G-test statistic were used to investigate HRV type spatial distribution. Demographic characteristics and clinical features of ARI were also compared. Results: Of 5,744 NPS samples collected, HRV was detected in 1057 (18.4%), of which 817 (77.3%) were successfully sequenced. HRV species A, B and C were identified in 360 (44.1%), 67 (8.2%) and 390 (47.7%) samples, respectively. In total, 87 types were determined: 39, 10 and 38 occurred within species A, B and C, respectively. HRV types presented heterogeneous temporal patterns of persistence. Spatially, identical types occurred over a wide distance at similar times, but there was statistically significant evidence for clustering of types between health facilities in close proximity or linked by major road networks. Conclusion: This study records a high prevalence of HRV in out-patient presentations exhibiting high type diversity. Patterns of occurrence suggest frequent and independent community invasion of different types. Temporal differences of persistence between types may reflect variation in type-specific population immunity. Spatial patterns suggest either rapid spread or multiple invasions of the same type, but evidence of similar types amongst close health facilities, or along road systems, indicate type partitioning structured by local spread.

Who interacts with whom? Social mixing insights from a rural population in India

Acute lower respiratory infections (ALRI) are a leading cause of morbidity and mortality globally, with most ALRI deaths occurring in children in developing countries. Computational models can be used to test the efficacy of respiratory infection prevention interventions, but require data on social mixing patterns, which are sparse in developing countries. We describe social mixing patterns among a rural community in northern India. During October 2015-February 2016, trained field workers conducted cross-sectional face-to-face standardized surveys in a convenience sample of 330 households in Faridabad District, Haryana State, India. Respondents were asked about the number, duration, and setting of social interactions during the previous 24 hours. Responses were compared by age and gender. Among the 3083 residents who were approached, 2943 (96%) participated, of whom 51% were male and the median age was 22 years (interquartile range (IQR) 9–37). Respondents reported contact (defined as having had a face-to-face conversation within 3 feet, which may or may not have included physical contact) with a median of 17 (IQR 12–25) people during the preceding 24 hours. Median total contact time per person was 36 person-hours (IQR 26–52). Female older children and adults had significantly fewer contacts than males of similar age (Kruskal-Wallis χ2 = 226.59, p<0.001), but spent a longer duration in contact with young children (Kruskal-Wallis χ2 = 27.26, p<0.001), suggesting a potentially complex pattern of differential risk of infection between genders. After controlling for household size and day of the week, respondent age was significantly associated with number and duration of contacts. These findings can be used to model the impact of interventions to reduce lower respiratory tract infections in India.

The role of neutrophils in the pathogenesis of Crohn's disease

Crohn's disease (CD) is caused by a trigger, almost certainly enteric infection by one of a multitude of organisms that allows faeces access to the tissues, at which stage the response of individuals predisposed to CD is abnormal. In CD the failure of acute inflammation results in the failure to recruit neutrophils to the inflammatory site, as a consequence of which the clearance of bacteria from the tissues is defective. The retained faecal products result in the characteristic chronic granulomatous inflammation and adaptive immune response. Impaired of digestion of bacteria and fungi by CGD neutrophils can result in a similar pathological and clinical picture. The neutrophils in CD are normal and their inadequate accumulation at sites of inflammation generally results from diminished secretion of proinflammatory cytokines by macrophages consequent upon disordered vesicle trafficking.

Human rhinovirus spatial-temporal epidemiology in rural coastal Kenya, 2015-2016, observed through outpatient surveillance

Background: Human rhinovirus (HRV) is the predominant cause of upper respiratory tract infections, resulting in a significant public health burden. The virus circulates as many different types (~160), each generating strong homologous, but weak heterotypic, immunity. The influence of these features on transmission patterns of HRV in the community is understudied. Methods: Nasopharyngeal swabs were collected from patients with symptoms of acute respiratory infection (ARI) at nine out-patient facilities across a Health and Demographic Surveillance System between December 2015 and November 2016. HRV was diagnosed by real-time RT-PCR, and the VP4/VP2 genomic region of the positive samples sequenced. Phylogenetic analysis was used to determine the HRV types. Classification models and G-test statistic were used to investigate HRV type spatial distribution. Demographic characteristics and clinical features of ARI were also compared. Results: Of 5,744 NPS samples collected, HRV was detected in 1057 (18.4%), of which 817 (77.3%) were successfully sequenced. HRV species A, B and C were identified in 360 (44.1%), 67 (8.2%) and 390 (47.7%) samples, respectively. In total, 87 types were determined: 39, 10 and 38 occurred within species A, B and C, respectively. HRV types presented heterogeneous temporal patterns of persistence. Spatially, identical types occurred over a wide distance at similar times, but there was statistically significant evidence for clustering of types between health facilities in close proximity or linked by major road networks. Conclusion: This study records a high prevalence of HRV in out-patient presentations exhibiting high type diversity. Patterns of occurrence suggest frequent and independent community invasion of different types. Temporal differences of persistence between types may reflect variation in type-specific population immunity. Spatial patterns suggest either rapid spread or multiple invasions of the same type, but evidence of similar types amongst close health facilities, or along road systems, indicate type partitioning structured by local spread.

An Agent-Based Metapopulation Model Simulating Virus-Based Biocontrol of Heterodera Glycines

With recently discovered soybean cyst nematode (SCN) viruses, biological control of the nematodes is a theoretical possibility. This study explores the question of what kinds of viruses would make useful biocontrol agents, taking into account evolutionary and population dynamics. An agent-based model, Soybean Cyst Nematode Simulation (SCNSim), was developed to simulate within-host virulence evolution in a virus-nematode-soybean ecosystem. SCNSim was used to predict nematode suppression under a range of viral mutation rates, initial virulences, and release strategies. The simulation model suggested that virus-based biocontrol worked best when the nematodes were inundated with the viruses. Under lower infection prevalence, the viral burden thinned out rapidly due to the limited mobility and high reproductive rate of the SCN. In accordance with the generally accepted trade-off theory, SCNSim predicted the optimal initial virulence for the maximum nematode suppression. Higher initial virulence resulted in shorter lifetime transmission, whereas viruses with lower initial virulence values evolved toward avirulence. SCNSim also indicated that a greater viral mutation rate reinforced the virulence pathotype, suggesting the presence of a virulence threshold necessary to achieve biocontrol against SCN.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

BACKGROUND

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.

SURVEY METHODOLOGY

In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.

RESULTS

We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.

DISCUSSION

Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Modeling the consequences of regional heterogeneity in human papillomavirus (HPV) vaccination uptake on transmission in Switzerland

BACKGROUND

Completed human papillomavirus (HPV) vaccination by age 16 years among women in Switzerland ranges from 17 to 75% across 26 cantons. The consequences of regional heterogeneity in vaccination coverage on transmission and prevalence of HPV-16 are unclear.

METHODS

We developed a deterministic, population-based model that describes HPV-16 transmission among young adults within and between the 26 cantons of Switzerland. We parameterized the model using sexual behavior data from Switzerland and data from the Swiss National Vaccination Coverage Survey. First, we investigated the general consequences of heterogeneity in vaccination uptake between two sub-populations. We then compared the predicted prevalence of HPV-16 resulting from heterogeneous HPV vaccination uptake in all of Switzerland with homogeneous vaccination at an uptake that is identical to the national average (52%).

RESULTS

In our baseline scenario, HPV-16 prevalence in women is 3.34% when vaccination is introduced and begins to diverge across cantons, ranging from 0.19 to 1.20% after 15 years of vaccination. After the same time period, overall prevalence of HPV-16 in Switzerland is only marginally higher (0.63%) with heterogeneous vaccination uptake than with homogeneous uptake (0.59%). Assuming inter-cantonal sexual mixing, cantons with low vaccination uptake benefit from a reduction in prevalence at the expense of cantons with high vaccination uptake.

CONCLUSIONS

Regional variations in uptake diminish the overall effect of vaccination on HPV-16 prevalence in Switzerland, but the effect size is small. Cantonal efforts towards HPV-prevalence reduction by increasing vaccination uptake are impaired by cantons with low vaccination uptake. Although the expected impact on national prevalence would be relatively small, harmonization of cantonal vaccination programs would reduce inter-cantonal differences in HPV-16 prevalence.

Master equations and the theory of stochastic path integrals

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

A stochastic model for MRSA transmission within a hospital ward incorporating environmental contamination

Methicillin-resistant Staphylococcus aureus (MRSA) transmission in hospital wards is associated with adverse outcomes for patients and increased costs for hospitals. The transmission process is inherently stochastic and the randomness emphasized by the small population sizes involved. As such, a stochastic model was proposed to describe the MRSA transmission process, taking into account the related contribution and modelling of the associated microbiological environmental contamination. The model was used to evaluate the performance of five common interventions and their combinations on six potential outcome measures of interest under two hypothetical disease burden settings. The model showed that the optimal intervention combination varied depending on the outcome measure and burden setting. In particular, it was found that certain outcomes only required a small subset of targeted interventions to control the outcome measure, while other outcomes still reported reduction in the outcome distribution with up to all five interventions included. This study describes a new stochastic model for MRSA transmission within a ward and highlights the use of the generalized Mann–Whitney statistic to compare the distribution of the outcome measures under different intervention combinations to assist in planning future interventions in hospital wards under different potential outcome measures and disease burden.

Stochastic epidemic dynamics on extremely heterogeneous networks

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.

Have We Substantially Underestimated the Impact of Improved Sanitation Coverage on Child Health? A Generalized Additive Model Panel Analysis of Global Data on Child Mortality and Malnutrition

BACKGROUND

Although widely accepted as being one of the most important public health advances of the past hundred years, the contribution that improving sanitation coverage can make to child health is still unclear, especially since the publication of two large studies of sanitation in India which found no effect on child morbidity. We hypothesis that the value of sanitation does not come directly from use of improved sanitation but from improving community coverage. If this is so we further hypothesise that the relationship between sanitation coverage and child health will be non-linear and that most of any health improvement will accrue as sanitation becomes universal.

METHODS

We report a fixed effects panel analysis of country level data using Generalized Additive Models in R. Outcome variables were under 5 childhood mortality, neonatal mortality, under 5 childhood mortality from diarrhoea, proportion of children under 5 with stunting and with underweight. Predictor variables were % coverage by improved sanitation, improved water source, Gross Domestic Product per capita and Health Expenditure per capita. We also identified three studies reporting incidence of diarrhoea in children under five alongside gains in community coverage in improved sanitation.

FINDINGS

For each of the five outcome variables, sanitation coverage was independently associated with the outcome but this association was highly non-linear. Improving sanitation coverage was very strongly associated with under 5 years diarrhoea mortality, under 5years all-cause mortality, and all-cause neonatal mortality. There was a decline as sanitation coverage increased up to about 20% but then no further decline was seen until about 70% (60% for diarrhoea mortality and 80% for neonatal mortality, respectively). The association was less strong for stunting and underweight but a threshold about 50% coverage was also seen. Three large trials of sanitation on diarrhoea morbidity gave results that were similar to what would have been predicted by our model.

CONCLUSIONS

Improving sanitation coverage may be one of the more effective means to reduce childhood mortality, but only if high levels of community coverage are achieved. Studies of the impact of sanitation that focus on the individual's use of improved sanitation as the predictor variable rather than community coverage is likely to severely underestimate the impact of sanitation.

Preserving privacy whilst maintaining robust epidemiological predictions

Mathematical models are invaluable tools for quantifying potential epidemics and devising optimal control strategies in case of an outbreak. State-of-the-art models increasingly require detailed individual farm-based and sensitive data, which may not be available due to either lack of capacity for data collection or privacy concerns. However, in many situations, aggregated data are available for use. In this study, we systematically investigate the accuracy of predictions made by mathematical models initialised with varying data aggregations, using the UK 2001 Foot-and-Mouth Disease Epidemic as a case study. We consider the scenario when the only data available are aggregated into spatial grid cells, and develop a metapopulation model where individual farms in a single subpopulation are assumed to behave uniformly and transmit randomly. We also adapt this standard metapopulation model to capture heterogeneity in farm size and composition, using farm census data. Our results show that homogeneous models based on aggregated data overestimate final epidemic size but can perform well for predicting spatial spread. Recognising heterogeneity in farm sizes improves predictions of the final epidemic size, identifying risk areas, determining the likelihood of epidemic take-off and identifying the optimal control strategy. In conclusion, in cases where individual farm-based data are not available, models can still generate meaningful predictions, although care must be taken in their interpretation and use.

Making sense of the cause of Crohn's - a new look at an old disease

The cause of Crohn’s disease (CD) has posed a conundrum for at least a century. A large body of work coupled with recent technological advances in genome research have at last started to provide some of the answers. Initially this review seeks to explain and to differentiate between bowel inflammation in the primary immunodeficiencies that generally lead to very early onset diffuse bowel inflammation in humans and in animal models, and the real syndrome of CD. In the latter, a trigger, almost certainly enteric infection by one of a multitude of organisms, allows the faeces access to the tissues, at which stage the response of individuals predisposed to CD is abnormal. Direct investigation of patients’ inflammatory response together with genome-wide association studies (GWAS) and DNA sequencing indicate that in CD the failure of acute inflammation and the clearance of bacteria from the tissues, and from within cells, is defective. The retained faecal products result in the characteristic chronic granulomatous inflammation and adaptive immune response. In this review I will examine the contemporary evidence that has led to this understanding, and look for explanations for the recent dramatic increase in the incidence of this disease.

Making sense of the cause of Crohn's - a new look at an old disease

The cause of Crohn's disease (CD) has posed a conundrum for at least a century. A large body of work coupled with recent technological advances in genome research have at last started to provide some of the answers. Initially this review seeks to explain and to differentiate between bowel inflammation in the primary immunodeficiencies that generally lead to very early onset diffuse bowel inflammation in humans and in animal models, and the real syndrome of CD. In the latter, a trigger, almost certainly enteric infection by one of a multitude of organisms, allows the faeces access to the tissues, at which stage the response of individuals predisposed to CD is abnormal. Direct investigation of patients' inflammatory response together with genome-wide association studies (GWAS) and DNA sequencing indicate that in CD the failure of acute inflammation and the clearance of bacteria from the tissues, and from within cells, is defective. The retained faecal products result in the characteristic chronic granulomatous inflammation and adaptive immune response. In this review I will examine the contemporary evidence that has led to this understanding, and look for explanations for the recent dramatic increase in the incidence of this disease.