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.

Dynamical analysis of a network-based SIR model with saturated incidence rate and nonlinear recovery rate: an edge-compartmental approach.

A new network-based SIR epidemic model with saturated incidence rate and nonlinear recovery rate is proposed. We adopt an edge-compartmental approach to rewrite the system as a degree-edge-mixed model. The explicit formula of the basic reproduction number $ \mathit{\boldsymbol{R_{0}}} $ is obtained by renewal equation and Laplace transformation. We find that $ \mathit{\boldsymbol{R_{0}}} < 1 $ is not enough to ensure global asymptotic stability of the disease-free equilibrium, and when $ \mathit{\boldsymbol{R_{0}}} > 1 $, the system can exist multiple endemic equilibria. When the number of hospital beds is small enough, the system will undergo backward bifurcation at $ \mathit{\boldsymbol{R_{0}}} = 1 $. Moreover, it is proved that the stability of feasible endemic equilibrium is determined by signs of tangent slopes of the epidemic curve. Finally, the theoretical results are verified by numerical simulations. This study suggests that maintaining sufficient hospital beds is crucial for the control of infectious diseases.

A Coupled Statistical and Deterministic Model for Forecasting Climate-Driven Dengue Incidence in Selangor, Malaysia.

The mosquito-borne dengue virus remains a major public health concern in Malaysia. Despite various control efforts and measures introduced by the Malaysian Government to combat dengue, the increasing trend of dengue cases persists and shows no sign of decreasing. Currently, early detection and vector control are the main methods employed to curb dengue outbreaks. In this study, a coupled model consisting of the statistical ARIMAX model and the deterministic SI-SIR model was developed and validated using the weekly reported dengue data from year 2014 to 2019 for Selangor, Malaysia. Previous studies have shown that climate variables, especially temperature, humidity, and precipitation, were able to influence dengue incidence and transmission dynamics through their effect on the vector. In this coupled model, climate is linked to dengue disease through mosquito biting rate, allowing real-time forecast of dengue cases using climate variables, namely temperature, rainfall and humidity. For the period chosen for model validation, the coupled model can forecast 1-2 weeks in advance with an average error of less than 6%, three weeks in advance with an average error of 7.06% and four weeks in advance with an average error of 8.01%. Further model simulation analysis suggests that the coupled model generally provides better forecast than the stand-alone ARIMAX model, especially at the onset of the outbreak. Moreover, the coupled model is more robust in the sense that it can be further adapted for investigating the effectiveness of various dengue mitigation measures subject to the changing climate.

A compartment and metapopulation model of Rocky Mountain spotted fever in southwestern United States and northern Mexico.

Rocky Mountain spotted fever (RMSF) is a fatal tick-borne zoonotic disease that has emerged as an epidemic in western North America since the turn of the 21st century. Along the US south-western border and across northern Mexico, the brown dog tick, Rhipicephalus sanguineus, is responsible for spreading the disease between dogs and humans. The widespread nature of the disease and the ongoing epidemics contrast with historically sporadic patterns of the disease. Because dogs are amplifying hosts for the Rickettsia rickettsii bacteria, transmission dynamics between dogs and ticks are critical for understanding the epidemic. In this paper, we developed a compartment metapopulation model and used it to explore the dynamics and drivers of RMSF in dogs and brown dog ticks in a theoretical region in western North America. We discovered that there is an extended lag-as much as two years-between introduction of the pathogen to a naïve population and epidemic-level transmission, suggesting that infected ticks could disseminate extensively before disease is detected. A single large city-size population of dogs was sufficient to maintain the disease over a decade and serve as a source for disease in surrounding smaller towns. This model is a novel tool that can be used to identify high risk areas and key intervention points for epidemic RMSF spread by brown dog ticks.

Excavating important nodes in complex networks based on the heat conduction model.

Analyzing the important nodes of complex systems by complex network theory can effectively solve the scientific bottlenecks in various aspects of these systems, and how to excavate important nodes has become a hot topic in complex network research. This paper proposes an algorithm for excavating important nodes based on the heat conduction model (HCM), which measures the importance of nodes by their output capacity. The number and importance of a node's neighbors are first used to determine its own capacity, its output capacity is then calculated based on the HCM while considering the network density, distance between nodes, and degree density of other nodes. The importance of the node is finally measured by the magnitude of the output capacity. The similarity experiments of node importance, sorting and comparison experiments of important nodes, and capability experiments of multi-node infection are conducted in nine real networks using the Susceptible-Infected-Removed model as the evaluation criteria. Further, capability experiments of multi-node infection are conducted using the Independent cascade model. The effectiveness of the HCM is demonstrated through a comparison with eight other algorithms for excavating important nodes.

R 0 May Not Tell Us Everything: Transient Disease Dynamics of Some SIR Models Over Patchy Environments.

This paper examines the short-term or transient dynamics of SIR infectious disease models in patch environments. We employ reactivity of an equilibrium and amplification rates, concepts from ecology, to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policy and decisions, and hence, these findings are of practical importance.

Simple economics of vaccination: public policies and incentives.

This paper focuses on the economics of vaccination and, more specifically, analyzes the vaccination decision of individuals using a game-theoretic model combined with an epidemiological SIR model that reproduces the infection dynamics of a generic disease. We characterize the equilibrium individual vaccination rate, and we show that it is below the rate compatible with herd immunity due to the existence of externalities that individuals do not internalize when they decide on vaccination. In addition, we analyze three public policies consisting of informational campaigns to reduce the disutility of vaccination, monetary payments to vaccinated individuals and measures to increase the disutility of non-vaccination. If the public authority uses only one type of policy, herd immunity is not necessarily achieved unless monetary incentives are used. When the public authority is not limited to use only one policy, we find that the optimal public policy should consist only of informational campaigns if they are sufficiently effective, or a combination of informational campaigns and monetary incentives otherwise. Surprisingly, the requirement of vaccine passports or other restrictions on the non-vaccinated are not desirable.

Assessing the impact of booster vaccination on diphtheria transmission: Mathematical modeling and risk zone mapping.

The COVID-19 pandemic caused significant disruptions in the healthcare system, affecting vaccinations and the management of diphtheria cases. As a consequence of these disruptions, numerous countries have experienced a resurgence or an increase in diphtheria cases. West Java province in Indonesia is identified as one of the high-risk areas for diphtheria, experiencing an upward trend in cases from 2021 to 2023. To analyze the situation, we developed an SIR model, which integrated DPT and booster vaccinations to determine the basic reproduction number, an essential parameter for infectious diseases. Through spatial analysis of geo-referenced data, we identified hotspots and explained diffusion in diphtheria case clusters. The calculation of R0 resulted in an R0 = 1.17, indicating the potential for a diphtheria outbreak in West Java. To control the increasing cases, one possible approach is to raise the booster vaccination coverage from the current 64.84% to 75.15%, as suggested by simulation results. Furthermore, the spatial analysis revealed that hot spot clusters were present in the western, central, and southern regions, posing a high risk not only in densely populated areas but also in rural regions. The diffusion pattern of diphtheria clusters displayed an expansion-contagious pattern. Understanding the rising trend of diphtheria cases and their geographic distribution can offer crucial insights for government and health authorities to manage the number of diphtheria cases and make informed decisions regarding the best prevention and intervention strategies.

Optimal intertemporal curative drug expenses: The case of hepatitis C in France.

We study intertemporal tradeoffs that health authorities face when considering the control of an epidemic using innovative curative medical treatments. We set up a dynamically controlled susceptible-infected-recovered (SIR) model for an epidemic in which patients can be asymptomatic, and we analyze the optimality conditions of the sequence of cure expenses decided by health authorities at the onset of the drug innovation process. We show that analytical conclusions are ambiguous because of their dependence on parameter values. As an application, we focus on the case study of hepatitis C, the treatment for which underwent a major upheaval when curative drugs were introduced in 2014. We calibrate our controlled SIR model using French data and simulate optimal policies. We show that the optimal policy entails some front loading of the intertemporal budget. The analysis demonstrates how beneficial intertemporal budgeting can be compared to non-forward-looking constant budget allocation.

Wording the trajectory of the three-year COVID-19 epidemic in a general population - Belgium.

The trajectory of COVID-19 epidemic waves in the general population of Belgium was analysed by defining quantitative criteria for epidemic waves from March 2020 to early 2023. Peaks and starting/ending times characterised nine waves numerated I to IX based on the daily reported incidence number (symbol INCID) and three "endemic" interval periods between the first four waves. The SIR compartmental model was applied to the first epidemic wave by fitting the daily prevalence pool (symbol I) calculated as the sum of the daily incidence rate and estimated number of subjects still infectious from the previous days. The basic reproductive number R0 was calculated based on the exponential growth rate during the early phase and on medical literature knowledge of the time of generation of SARS-CoV-2 infection. The first COVID-19 wave was well fitted by an open SIR model. According to this approach, dampened recurrent epidemic waves evolving through an endemic state would have been expected. This was not the case with the subsequent epidemic waves being characterised by new variants of concern (VOC). Evidence-based observations: 1) each epidemic wave affected less than a fifth of the general population; 2) the Vth epidemic wave (VOC Omicron) presented the greatest amplitude. The lack of recurrence of the same VOC during successive epidemic waves strongly suggests that a VOC has a limited persistence, disappearing from the population well before the expected proportion of the theoretical susceptible cohort being maximally infected. Fitting the theoretical SIR model, a limited persistence of VOCs in a population could explain that new VOCs replace old ones, even if the new VOC has a lower transmission rate than the preceding one. In conclusion, acquisition of potential defective mutations in VOC during an epidemic wave is a potential factor explaining the absence of resurgence of a same VOC during successive waves. Such an hypothesis is open to discussion and to rebuttal. A modified SIR model with epidemic waves of variable amplitude related not only to R0 and public health measures but also to acquisition of defective fitting in virus within a population should be tested.

Assessing the impact of isolation policies on epidemic dynamics through swarm entropy.

Isolation policies are an effective measure in epidemiological models for the prediction and prevention of infectious diseases. In this paper, we use a multi-agent modeling approach to construct an infectious disease model that considers the influence of isolation policies. The model analyzes the impact of isolation policies on various stages of epidemic from two perspectives: the external environment and agents behavior. It utilizes multiple variables to simulate the extent to which isolation policies influence the spread of the pandemic. Empirical evidence indicates that the progression of the epidemic is primarily driven by factors such as public willingness and regulatory intensity. The improved model, in comparison to traditional infectious disease models, offers greater flexibility and accuracy, addressing the need for frequent modifications in fundamental models within complex environments. Meanwhile, we introduce "swarm entropy" to evaluate infection intensity under various policies. By linking isolation policies with swarm entropy, considering population structure, we quantify the effectiveness of these isolation measures. It provides a novel approach for complex population simulations. These findings have facilitated the enhancement of control strategies and provided decision-makers with guidance in combating the transmission of infectious diseases.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

Modeling and Analyzing Xylem Vulnerability to Embolism as an Epidemic Process.

Xylem vulnerability to embolism can be quantified by "vulnerability curves" (VC) that are obtained by subjecting wood samples to increasingly negative water potential and monitoring the progressive loss of hydraulic conductivity. VC are typically sigmoidal, and various approaches are used to fit the experimentally obtained VC data for extracting benchmark data of vulnerability to embolism. In addition to such empirical methods, mechanistic approaches to calculate embolism propagation are epidemic modeling and network theory. Both describe the transmission of "objects" (in this case, the transmission of gas) between interconnected elements. In network theory, a population of interconnected elements is described by graphs in which objects are represented by vertices or nodes and connections between these objections as edges linking the vertices. A graph showing a population of interconnected xylem conduits represents an "individual" wood sample that allows spatial tracking of embolism propagation. In contrast, in epidemic modeling, the transmission dynamics for a population that is subdivided into infection-relevant groups is calculated by an equation system. For this, embolized conduits are considered to be "infected," and the "infection" is the transmission of gas from embolized conduits to their still water-filled neighbors. Both approaches allow for a mechanistic simulation of embolism propagation.

Non-smooth dynamics of a SIR model with nonlinear state-dependent impulsive control.

The classic SIR model is often used to evaluate the effectiveness of controlling infectious diseases. Moreover, when adopting strategies such as isolation and vaccination based on changes in the size of susceptible populations and other states, it is necessary to develop a non-smooth SIR infectious disease model. To do this, we first add a non-linear term to the classical SIR model to describe the impact of limited medical resources or treatment capacity on infectious disease transmission, and then involve the state-dependent impulsive feedback control, which is determined by the convex combinations of the size of the susceptible population and its growth rates, into the model. Further, the analytical methods have been developed to address the existence of non-trivial periodic solutions, the existence and stability of a disease-free periodic solution (DFPS) and its bifurcation. Based on the properties of the established Poincaré map, we conclude that DFPS exists, which is stable under certain conditions. In particular, we show that the non-trivial order-1 periodic solutions may exist and a non-trivial order-$ k $ ($ k\geq 1 $) periodic solution in some special cases may not exist. Moreover, the transcritical bifurcations around the DFPS with respect to the parameters $ p $ and $ AT $ have been investigated by employing the bifurcation theorems of discrete maps.

Fundamental bound on epidemic overshoot in the SIR model.

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at [Formula: see text]. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

Viral Respiratory Epidemic Modeling of Societal Segregation Based on Vaccination Status.

BACKGROUND: Societal segregation of unvaccinated people from public spaces has been a novel and controversial coronavirus disease 2019 (COVID-19)-era public health practice in many countries. Models exploring potential consequences of vaccination-status-based segregation have not considered how segregation influences the contact frequencies in the segregated groups. We systematically investigate implementing effects of segregation on population-specific contact frequencies and show this critically determines the predicted epidemiological outcomes, focusing on the attack rates in the vaccinated and unvaccinated populations and the share of infections among vaccinated people that were due to contacts with infectious unvaccinated people. METHODS: We describe a susceptible-infectious-recovered (SIR) two-population model for vaccinated and unvaccinated groups of individuals that transmit an infectious disease by person-to-person contact. The degree of segregation of the two groups, ranging from zero to complete segregation, is implemented using the like-to-like mixing approach developed for sexually transmitted diseases, adapted for presumed severe acute respiratory syndrome coronavirus 2 (SARS­CoV­2) transmission. We allow the contact frequencies for individuals in the two groups to be different and depend, with variable strength, on the degree of segregation. RESULTS: Segregation can either increase or decrease the attack rate among the vaccinated, depending on the type of segregation (isolating or compounding), and the contagiousness of the disease. For diseases with low contagiousness, segregation can cause an attack rate in the vaccinated, which does not occur without segregation. INTERPRETATION: There is no predicted blanket epidemiological advantage to segregation, either for the vaccinated or the unvaccinated. Negative epidemiological consequences can occur for both groups.

Estimating the prevalence of COVID-19 cases through the analysis of SARS-CoV-2 RNA copies derived from wastewater samples from North Dakota.

The SARS-CoV-2 virus was first detected in December 2019, which prompted many researchers to investigate how the virus spreads. SARS-CoV-2 is mainly transmitted through respiratory droplets. Symptoms of the SARS-CoV-2 virus appear after an incubation period. Moreover, the asymptomatic infected individuals unknowingly spread the virus. Detecting infected people requires daily tests and contact tracing, which are expensive. The early detection of infectious diseases, including COVID-19, can be achieved with wastewater-based epidemiology, which is timely and cost-effective. In this study, we collected wastewater samples from wastewater treatment plants in several cities in North Dakota and then extracted viral RNA copies. We used log-RNA copies in the model to predict the number of infected cases using Quantile Regression (QR) and K-Nearest Neighbor (KNN) Regression. The model's performance was evaluated by comparing the Mean Absolute Percentage Error (MAPE). The QR model performs well in cities where the population is >10000. In addition, the model predictions were compared with the basic Susceptible-Infected-Recovered (SIR) model which is the golden standard model for infectious diseases.

Analytical tool for COVID-19 using an SIR model equivalent to the chain reaction equation of infection.

Insights from data analysis of existing cases are important to prevent future outbreaks of coronavirus disease 2019 (COVID-19). Although mathematical models are expected to be useful for this purpose, the adequacy of reproducibility of these models is difficult to confirm because they are based on hypotheses. For example, using the time variation of the parameter of the basic reproduction number for the time variation of complex data on the number of infected persons is a change of expression and does not capture the substance of the problem. We previously showed that the simplest Susceptible, Infected, Recovered (SIR) model alone, without any complex models, exhibits acceptable reproducibility. By clarifying the rationale for this reproducibility, quantifiable characteristics regarding the infection spread, such as the duration of the pandemic and the mechanism of occurrence of several large waves, can be uncovered and this can contribute to countermeasures. Here, we show this method equals the chain reaction equation for infection, allowing the parameters (infection rate, population) of the mathematical models to be extracted from the data. Once a model that reproduces the actual situation is determined, much of the information becomes apparent. As an example, we present three characteristics of the spread of infection effective in controlling COVID-19: the time of onset of infection, the rapidity of the spread, and the time to acquisition of herd immunity. Acquiring this information is likely to increase the predictive accuracy of the model.

Comparison of homemade mask designs based on calculated infection risk, using actual COVID-19 infection scenarios.

During pandemics such as COVID-19, shortages of approved respirators necessitate the use of alternative masks, including homemade designs. The effectiveness of the masks is often quantified in terms of the ability to filter particles. However, to formulate public policy the efficacy of the mask in reducing the risk of infection for a given population is considerably more useful than its filtration efficiency (FE). The effect of the mask on the infection profile is complicated to estimate as it depends strongly upon the behavior of the affected population. A recently introduced tool known as the dynamic-spread model is well suited for performing population-specific risk assessment. The dynamic-spread model was used to simulate the performance of a variety of mask designs (all used for source control only) in different COVID-19 scenarios. The efficacy of different masks was found to be highly scenario dependent. Switching from a cotton T-shirt of 8% FE to a 3-layer cotton-gauze-cotton mask of 44% FE resulted in a decrease in number of new infections of about 30% in the New York State scenario and 60% in the Harris County, Texas scenario. The results are valuable to policy makers for quantifying the impact upon the infection rate for different intervention strategies, e.g., investing resources to provide the community with higher-filtration masks.

A Congressional Twitter network dataset quantifying pairwise probability of influence.

We present a social network dataset based on interactions between members of the 117th United States Congress between Feb. 9, 2022, and June 9, 2022. The dataset takes the form of a directed, weighted network in which the edge weights are empirically obtained "probabilities of influence" between all pairs of Congresspeople. Twitter's application programming interface (API) V2 was used to determine the number of times each member of Congress retweeted, quote tweeted, replied to, or mentioned other Congressional members, and the probability of influence was found by normalizing the summed influence by the number of tweets issued by each Congressperson. This network may be of particular interest to the study of information diffusion within social networks.