Carl Flügge, one of the last holistic hygienists and discoverer of droplet transmission of infectious diseases.

Carl Flügge is best known for the promotion of studies demonstrating the transmission of all manner of infections, but particularly tuberculosis, by coughed droplets. But it is seldom recognised that Flügge was also influential in a number of other fields comprising the practice of hygiene. One-hundred years following his death in 1923, we review literature related to the studies of Flügge and his colleagues and students and illustrate the particular emphasis he laid upon the environment within which disease and its transmission might be fostered or prevented, embracing and studying aspects essential to the health of any community ranging from fundamental microbiology in the laboratory to subjects as disparate as housing, clean water supply, nutrition, sanitation, socio-economic circumstances and climate. Very early in his career he promoted breast feeding for the prevention of seasonal gastro-enteritis and later the sheltering of cough as a means of preventing the transmission of infected respiratory droplets, not only as regards tuberculosis, but also concerning all manner of other respiratory infections. By the time of Flügge's death the complexification of available scientific methodologies comprising hygiene made it difficult for any individual to comprehend and study the wide range of hygiene-related subjects such as Flügge did. Carl Flügge was one of the last holistic hygienists and an originator of the study of environmental health as a pillar of hygiene.

A novel method to select time-varying multivariate time series models for the surveillance of infectious diseases.

BACKGROUND: Describing the transmission dynamics of infectious diseases across different regions is crucial for effective disease surveillance. The multivariate time series (MTS) model has been widely adopted for constructing cross-regional infectious disease transmission networks due to its strengths in interpretability and predictive performance. Nevertheless, the assumption of constant parameters frequently disregards the dynamic shifts in disease transmission rates, thereby compromising the accuracy of early warnings. This study investigated the applicability of time-varying MTS models in multi-regional infectious disease monitoring and explored strategies for model selection. METHODS: This study focused on two prominent time-varying MTS models: the time-varying parameter-stochastic volatility-vector autoregression (TVP-SV-VAR) model and the time-varying VAR model using the generalized additive framework (tvvarGAM), and intended to explore and verify their applicable conditions for the surveillance of infectious diseases. For the first time, this study proposed the time delay coefficient and spatial sparsity indicators for model selection. These indicators quantify the temporal lags and spatial distribution of infectious disease data, respectively. Simulation study adopted from real-world infectious disease surveillance was carried out to compare model performances under various scenarios of spatio-temporal variation as well as random volatility. Meanwhile, we illustrated how the modelling process could help the surveillance of infectious diseases with an application to the influenza-like case in Sichuan Province, China. RESULTS: When the spatio-temporal variation was small (time delay coefficient: 0.1-0.2, spatial sparsity:0.1-0.3), the TVP-SV-VAR model was superior with smaller fitting residuals and standard errors of parameter estimation than those of the tvvarGAM model. In contrast, the tvvarGAM model was preferable when the spatio-temporal variation increased (time delay coefficient: 0.2-0.3, spatial sparsity: 0.6-0.9). CONCLUSION: This study emphasized the importance of considering spatio-temporal variations when selecting appropriate models for infectious disease surveillance. By incorporating our novel indicators-the time delay coefficient and spatial sparsity-into the model selection process, the study could enhance the accuracy and effectiveness of infectious disease monitoring efforts. This approach was not only valuable in the context of this study, but also has broader implications for improving time-varying MTS analyses in various applications.

The impact of population influx on infectious diseases - from the mediating effect of polluted air transmission.

The global population influx during the COVID-19 pandemic poses significant challenges to public health, making the prevention and control of infectious diseases a pressing concern. This paper aims to examine the impact of population influx on the spread of infectious diseases, with a specific emphasis on the mediating role of air pollution in this process. A theoretical analysis is conducted to explore the relationship between population influx, air pollution, and infectious diseases. Additionally, we establish a series of econometric models and employ various empirical tests and analytical techniques, including mediation effect test, threshold effect test, and systematic GMM test, to evaluate our hypotheses. The results indicate that: (1) Population influx directly and indirectly impacts infectious diseases. Specifically, population influx not only directly elevates the risk of infectious diseases, but also indirectly increases the incidence rate of infectious diseases by intensifying air pollution. (2) The impact of population inflow on infectious diseases exhibits regional heterogeneity. Compared to central and western China, the eastern regions exhibit a significantly higher risk of infectious diseases, exceeding the national average. (3) External factors influence the relationship between population influx and infectious diseases differently. Personal income and medical resources both help mitigate the risk of infectious diseases due to population influx, with medical resources having a more substantial effect. Contrary to expectations, abundant educational resources have not reduced the risk, instead, they have exacerbated the risk associated with population influx. This paper provides a scientific basis for formulating effective strategies for the prevention and control of infectious diseases.

Effect of individual activity level heterogeneity on disease spreading in higher-order networks.

The active state of individuals has a significant impact on disease spread dynamics. In addition, pairwise interactions and higher-order interactions coexist in complex systems, and the pairwise networks proved insufficient for capturing the essence of complex systems. Here, we propose a higher-order network model to study the effect of individual activity level heterogeneity on disease-spreading dynamics. Activity level heterogeneity radically alters the dynamics of disease spread in higher-order networks. First, the evolution equations for infected individuals are derived using the mean field method. Second, numerical simulations of artificial networks reveal that higher-order interactions give rise to a discontinuous phase transition zone where the coexistence of health and disease occurs. Furthermore, the system becomes more unstable as individual activity levels rise, leading to a higher likelihood of disease outbreaks. Finally, we simulate the proposed model on two real higher-order networks, and the results are consistent with the artificial networks and validate the inferences from theoretical analysis. Our results explain the underlying reasons why groups with higher activity levels are more likely to initiate social changes. Simultaneously, the reduction in group activity, characterized by measures such as "isolation," emerges as a potent strategy for disease control.

Tackling transmission of infectious diseases: A probiotic-based system as a remedy for the spread of pathogenic and resistant microbes.

Built environments (BEs) currently represent the areas in which human beings spend most of their life. Consistently, microbes populating BEs mostly derive from human occupants and can be easily transferred from BE to occupants. The hospital microbiome is a paradigmatic example, representing a reservoir for harmful pathogens that can be transmitted to susceptible patients, causing the healthcare-associated infections (HAIs). Environmental cleaning is a crucial pillar in controlling BE pathogens and preventing related infections, and chemical disinfectants have been largely used so far towards this aim. However, despite their immediate effect, chemical-based disinfection is unable to prevent recontamination, has a high environmental impact, and can select/increase antimicrobial resistance (AMR) in treated microbes. To overcome these limitations, probiotic-based sanitation (PBS) strategies were recently proposed, built on the use of detergents added with selected probiotics able to displace surrounding pathogens by competitive exclusion. PBS was reported as an effective and low-impact alternative to chemical disinfection, providing stable rebalance of the BE microbiome and significantly reducing pathogens and HAIs compared to disinfectants, without exacerbating AMR and pollution concerns. This minireview summarizes the most significant results obtained by applying PBS in sanitary and non-sanitary settings, which overall suggest that PBS may effectively tackle the infectious risk meanwhile preventing the further spread of pathogenic and resistant microbes.

Impact of infectious diseases on wild bovidae populations in Thailand: insights from population modelling and disease dynamics.

The wildlife and livestock interface is vital for wildlife conservation and habitat management. Infectious diseases maintained by domestic species may impact threatened species such as Asian bovids, as they share natural resources and habitats. To predict the population impact of infectious diseases with different traits, we used stochastic mathematical models to simulate the population dynamics over 100 years for 100 times in a model gaur (Bos gaurus) population with and without disease. We simulated repeated introductions from a reservoir, such as domestic cattle. We selected six bovine infectious diseases; anthrax, bovine tuberculosis, haemorrhagic septicaemia, lumpy skin disease, foot and mouth disease and brucellosis, all of which have caused outbreaks in wildlife populations. From a starting population of 300, the disease-free population increased by an average of 228% over 100 years. Brucellosis with frequency-dependent transmission showed the highest average population declines (-97%), with population extinction occurring 16% of the time. Foot and mouth disease with frequency-dependent transmission showed the lowest impact, with an average population increase of 200%. Overall, acute infections with very high or low fatality had the lowest impact, whereas chronic infections produced the greatest population decline. These results may help disease management and surveillance strategies support wildlife conservation.

Social vs. individual age-dependent costs of imperfect vaccination.

In diseases with long-term immunity, vaccination is known to increase the average age at infection as a result of the decrease in the pathogen circulation. This implies that a vaccination campaign can have negative effects when a disease is more costly (financial or health-related costs) for higher ages. This work considers an age-structured population transmission model with imperfect vaccination. We aim to compare the social and individual costs of vaccination, assuming that disease costs are age-dependent, while the disease's dynamic is age-independent. A model for pathogen deterministic dynamics in a population consisting of juveniles and adults, assumed to be rational agents, is introduced. The parameter region for which vaccination has a positive social impact is fully characterized and the Nash equilibrium of the vaccination game is obtained. Finally, collective strategies designed to promote voluntary vaccination, without compromising social welfare, are discussed.

Detecting and quantifying heterogeneity in susceptibility using contact tracing data.

The presence of heterogeneity in susceptibility, differences between hosts in their likelihood of becoming infected, can fundamentally alter disease dynamics and public health responses, for example, by changing the final epidemic size, the duration of an epidemic, and even the vaccination threshold required to achieve herd immunity. Yet, heterogeneity in susceptibility is notoriously difficult to detect and measure, especially early in an epidemic. Here we develop a method that can be used to detect and estimate heterogeneity in susceptibility given contact by using contact tracing data, which are typically collected early in the course of an outbreak. This approach provides the capability, given sufficient data, to estimate and account for the effects of this heterogeneity before they become apparent during an epidemic. It additionally provides the capability to analyze the wealth of contact tracing data available for previous epidemics and estimate heterogeneity in susceptibility for disease systems in which it has never been estimated previously. The premise of our approach is that highly susceptible individuals become infected more often than less susceptible individuals, and so individuals not infected after appearing in contact networks should be less susceptible than average. This change in susceptibility can be detected and quantified when individuals show up in a second contact network after not being infected in the first. To develop our method, we simulated contact tracing data from artificial populations with known levels of heterogeneity in susceptibility according to underlying discrete or continuous distributions of susceptibilities. We analyzed these data to determine the parameter space under which we are able to detect heterogeneity and the accuracy with which we are able to estimate it. We found that our power to detect heterogeneity increases with larger sample sizes, greater heterogeneity, and intermediate fractions of contacts becoming infected in the discrete case or greater fractions of contacts becoming infected in the continuous case. We also found that we are able to reliably estimate heterogeneity and disease dynamics. Ultimately, this means that contact tracing data alone are sufficient to detect and quantify heterogeneity in susceptibility.

Multiple endemic equilibria in an environmentally-transmitted disease with three disease stages.

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

Infection thresholds for two interacting pathogens in a wild animal population.

We present a model for the dynamics of two interacting pathogen variants in a wild animal host population. Using the next-generation matrix approach we define the invasion threshold for one pathogen variant when the other is already established and at steady state. We then provide explicit criteria for the special cases where: i) the two pathogen variants exclude each other; ii) one variant excludes the other; iii) the population dynamics of hosts infected with both variants are independent of the order of infection; iv) there is no interaction between the variants; and v) one variant enhances transmission of the other.

Fitting Epidemic Models to Data: A Tutorial in Memory of Fred Brauer.

Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.

Modeling the transmission mitigation impact of testing for infectious diseases.

A fundamental question of any program focused on the testing and timely diagnosis of a communicable disease is its effectiveness in reducing transmission. Here, we introduce testing effectiveness (TE)-the fraction by which testing and post-diagnosis isolation reduce transmission at the population scale-and a model that incorporates test specifications and usage, within-host pathogen dynamics, and human behaviors to estimate TE. Using TE to guide recommendations, we show that today's rapid diagnostics should be used immediately upon symptom onset to control influenza A and respiratory syncytial virus but delayed by up to two days to control omicron-era severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furthermore, while rapid tests are superior to reverse transcription quantitative polymerase chain reaction (RT-qPCR) to control founder-strain SARS-CoV-2, omicron-era changes in viral kinetics and rapid test sensitivity cause a reversal, with higher TE for RT-qPCR despite longer turnaround times. Last, we illustrate the model's flexibility by quantifying trade-offs in the use of post-diagnosis testing to shorten isolation times.

Infection patterns in simple and complex contagion processes on networks.

Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the network structure on spreading process has been widely investigated, but not the reverse question: do different processes unfolding on a given network lead to different infection patterns? How do the infection patterns depend on a model's parameters or on the nature of the contagion processes? Here we address this issue by investigating the infection patterns for a variety of models. In simple contagion processes, where contagion events involve one connection at a time, we find that the infection patterns are extremely robust across models and parameters. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on models parameters emerge, as the infection pattern depends on the interplay between pairwise and group contagions. In models involving threshold mechanisms moreover, slight parameter changes can significantly impact the spreading paths. Our results show that it is possible to study crucial features of a spread from schematized models, and inform us on the variations between spreading patterns in processes of different nature.

Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

Approximating reproduction numbers: a general numerical method for age-structured models.

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources.

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e., the basic reproduction number $ R_0/ $, which completely determines the dynamics of disease: when $ R_0/ < 1 $, the disease is eradicated; while when $ R_0/ > 1 $, the disease is persistent. To validate our theoretical findings, we conducted some numerical simulations using actual parameter values of COVID-19. Both our theoretical and simulation results indicated that (1) the white noise can significantly affect the dynamics of a disease, and importantly, it can shift the stability of the disease-free equilibrium; (2) infectious disease resurgence may be caused by random switching of the environment; and (3) it is vital to maintain adequate healthcare resources to control the spread of disease.

Comprehensive profiling of social mixing patterns in resource poor countries: A mixed methods research protocol.

BACKGROUND: Low-and-middle-income countries (LMICs) bear a disproportionate burden of communicable diseases. Social interaction data inform infectious disease models and disease prevention strategies. The variations in demographics and contact patterns across ages, cultures, and locations significantly impact infectious disease dynamics and pathogen transmission. LMICs lack sufficient social interaction data for infectious disease modeling. METHODS: To address this gap, we will collect qualitative and quantitative data from eight study sites (encompassing both rural and urban settings) across Guatemala, India, Pakistan, and Mozambique. We will conduct focus group discussions and cognitive interviews to assess the feasibility and acceptability of our data collection tools at each site. Thematic and rapid analyses will help to identify key themes and categories through coding, guiding the design of quantitative data collection tools (enrollment survey, contact diaries, exit survey, and wearable proximity sensors) and the implementation of study procedures. We will create three age-specific contact matrices (physical, nonphysical, and both) at each study site using data from standardized contact diaries to characterize the patterns of social mixing. Regression analysis will be conducted to identify key drivers of contacts. We will comprehensively profile the frequency, duration, and intensity of infants' interactions with household members using high resolution data from the proximity sensors and calculating infants' proximity score (fraction of time spent by each household member in proximity with the infant, over the total infant contact time) for each household member. DISCUSSION: Our qualitative data yielded insights into the perceptions and acceptability of contact diaries and wearable proximity sensors for collecting social mixing data in LMICs. The quantitative data will allow a more accurate representation of human interactions that lead to the transmission of pathogens through close contact in LMICs. Our findings will provide more appropriate social mixing data for parameterizing mathematical models of LMIC populations. Our study tools could be adapted for other studies.

An SEIR network epidemic model with manual and digital contact tracing allowing delays.

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network contact is reported, tested and isolated with some probability and after a random delay. Additionally, digital tracing (based on a tracing app) is triggered if the diagnosed individual is an app-user, and then all of its app-using infectees are immediately notified and isolated. The early phase of the epidemic with manual and/or digital tracing is approximated by different multi-type branching processes, and three respective reproduction numbers are derived. The effectiveness of both contact tracing mechanisms is numerically quantified through the reduction of the reproduction number. This shows that app-using fraction plays an essential role in the overall effectiveness of contact tracing. The relative effectiveness of manual tracing compared to digital tracing increases if: more of the transmission occurs on the network, when the tracing delay is shortened, and when the network degree distribution is heavy-tailed. For realistic values, the combined tracing case can reduce R0 by 20%-30%, so other preventive measures are needed to reduce the reproduction number down to 1.2-1.4 for contact tracing to make it successful in avoiding big outbreaks.

Optimal control of a fractional order SEIQR epidemic model with non-monotonic incidence and quarantine class.

During any infectious disease outbreak, effective and timely quarantine of infected individuals, along with preventive measures by the population, is vital for controlling the spread of infection in society. Therefore, this study attempts to provide a mathematically validated approach for managing the epidemic spread by incorporating the Monod-Haldane incidence rate, which accounts for psychological effects, and a saturated quarantine rate as Holling functional type III that considers the limitation in quarantining of infected individuals into the standard Susceptible-Exposed-Infected-Quarantine-Recovered (SEIQR) model. The rate of change of each subpopulation is considered as the Caputo form of fractional derivative where the order of derivative represents the memory effects in epidemic transmission dynamics and can enhance the accuracy of disease prediction by considering the experience of individuals with previously encountered. The mathematical study of the model reveals that the solutions are well-posed, ensuring nonnegativity and boundedness within an attractive region. Further, the study identifies two equilibria, namely, disease-free (DFE) and endemic (EE); and stability analysis of equilibria is performed for local as well as global behaviours for the same. The stability behaviours of equilibria mainly depend on the basic reproduction number R0 and its alternative threshold T0 which is computed using the Next-generation matrix method. It is investigated that DFE is locally and globally asymptotic stable when R0<1. Furthermore, we show the existence of EE and investigate that it is locally and globally asymptotic stable using the Routh-Hurwitz criterion and the Lyapunov stability theorem for fractional order systems with R0>1 under certain conditions. This study also addresses a fractional optimal control problem (FOCP) using Pontryagin's maximum principle aiming to minimize the spread of infection with minimal expenditure. This approach involves introducing a time-dependent control measure, u(t), representing the behavioural response of susceptible individuals. Finally, numerical simulations are presented to support the analytical findings using the Adams Bashforth Moulton scheme in MATLAB, providing a comprehensive understanding of the proposed SEIQR model.

Phylogenetic inference of inter-population transmission rates for infectious diseases.

Estimating transmission rates is a challenging yet essential aspect of comprehending and controlling the spread of infectious diseases. Various methods exist for estimating transmission rates, each with distinct assumptions, data needs, and constraints. This study introduces a novel phylogenetic approach called transRate, which integrates genetic information with traditional epidemiological approaches to estimate inter-population transmission rates. The phylogenetic method is statistically consistent as the sample size (i.e. the number of pathogen genomes) approaches infinity under the multi-population susceptible-infected-recovered model. Simulation analyses indicate that transRate can accurately estimate the transmission rate with a sample size of 200 ~ 400 pathogen genomes. Using transRate, we analyzed 40,028 high-quality sequences of SARS-CoV-2 in human hosts during the early pandemic. Our analysis uncovered significant transmission between populations even before widespread travel restrictions were implemented. The development of transRate provides valuable insights for scientists and public health officials to enhance their understanding of the pandemic's progression and aiding in preparedness for future viral outbreaks. As public databases for genomic sequences continue to expand, transRate is increasingly vital for tracking and mitigating the spread of infectious diseases.