Correcting the actual reproduction number: a simple method to estimate R(0) from early epidemic growth data

Analysis of the impact of COVID-19 variants and vaccination on the time-varying reproduction number: statistical methods

Introduction

The COVID-19 pandemic has profoundly impacted global health systems, requiring the monitoring of infection waves and strategies to control transmission. Estimating the time-varying reproduction number is crucial for understanding the epidemic and guiding interventions.

Methods

Probability distributions of serial interval are estimated for Pre-Delta and Delta periods. We conducted a comparative analysis of time-varying reproduction numbers, taking into account population immunity and variant differences. We incorporated the regional heterogeneity and age distribution of the population, as well as the evolving variants and vaccination rates over time. COVID-19 transmission dynamics were analyzed with variants and vaccination.

Results

The reproduction number is computed with and without considering variant-based immunity. In addition, values of reproduction number significantly differed by variants, emphasizing immunity's importance. Enhanced vaccination efforts and stringent control measures were effective in reducing the transmission of the Delta variant. Conversely, Pre-Delta variant appeared less influenced by immunity levels, due to lower vaccination rates. Furthermore, during the Pre-Delta period, there was a significant difference between the region-specific and the non-region-specific reproduction numbers, with particularly distinct pattern differences observed in Gangwon, Gyeongbuk, and Jeju in Korea.

Discussion

This research elucidates the dynamics of COVID-19 transmission concerning the dominance of the Delta variant, the efficacy of vaccinations, and the influence of immunity levels. It highlights the necessity for targeted interventions and extensive vaccination coverage. This study makes a significant contribution to the understanding of disease transmission mechanisms and informs public health strategies.

SARS-CoV-2 incidence monitoring and statistical estimation of the basic and time-varying reproduction number at the early onset of the pandemic in 45 sub-Saharan African countries

The world battled to defeat a novel coronavirus 2019 (SARS-CoV-2 or COVID-19), a respiratory illness that is transmitted from person to person through contacts with droplets from infected persons. Despite efforts to disseminate preventable messages and adoption of mitigation strategies by governments and the World Health Organization (WHO), transmission spread globally. An accurate assessment of the transmissibility of the coronavirus remained a public health priority for many countries across the world to fight this pandemic, especially at the early onset. In this paper, we estimated the transmission potential of COVID-19 across 45 countries in sub-Saharan Africa using three approaches, namely, [Formula: see text] based on (i) an exponential growth model (ii) maximum likelihood (ML) estimation and (iii) a time-varying basic reproduction number at the early onset of the pandemic. Using data from March 14, 2020, to May 10, 2020, sub-Saharan African countries were still grappling with COVID-19 at that point in the pandemic. The region's basic reproduction number ([Formula: see text]) was 1.89 (95% CI: 1.767 to 2.026) using the growth model and 1.513 (95% CI: 1.491 to 1.535) with the maximum likelihood method, indicating that, on average, infected individuals transmitted the virus to less than two secondary persons. Several countries, including Sudan ([Formula: see text]: 2.03), Ghana ([Formula: see text]: 1.87), and Somalia ([Formula: see text]: 1.85), exhibited high transmission rates. These findings highlighted the need for continued vigilance and the implementation of effective control measures to combat the pandemic in the region. It is anticipated that the findings in this study would not only function as a historical record of reproduction numbers during the COVID-19 pandemic in African countries, but can serve as a blueprint for addressing future pandemics of a similar nature.

Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington-DeAngelis incidence rate and Holling type II treatment. The superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and the basic reproductive number is calculated. The sensitivity analysis of the basic reproductive number is presented, and we show that some parameters strongly influence the dynamics of the system. A bifurcation analysis to determine the direction and stability of the model is carried out using the normal form and center manifold theorem. The results reveal a proportionality between the transmission delay and the diffusion rate. The numerical results show the formation of patterns in the model, and their epidemiological implications are discussed.

HIV screening and linkage to care in a health department in Valencia, Spain: Lessons learned from a healthcare quality improvement project

Spain's rate of new human immunodeficiency virus (HIV) diagnoses exceeds that of the European Economic Area average (8.6 vs 5.6:100,000 in 2018). The country has failed to meet the first of United Nations Programme on HIV/AIDS (UNAIDS) 90-90-90 targets for HIV control by 2020, with 87.0% of people living with HIV knowing their status, and late presentation rates of 47.6% and 51.5% country-wide and in the Valencian autonomous community, respectively. Advancing screening and linkage to care (SLTC) practices is necessary to effectively control the epidemic. The Valencia Viral Screening (CRIVALVIR) project adopted the TEST model for opportunistic and systematic HIV SLTC in individuals aged 18 to 80 who required blood work for any purpose, as of February 2019. SLTC was integrated into routine clinical workflow across primary care centers serving a population of 360,000 people in Valencia, Spain. Our project successfully upscaled total HIV testing by 194% to over 32,000 patients tested in 14 months. We found an overall prevalence of 0.13% (0.08-0.21) among those screened per protocol (n = 13,061), with foreign-born citizens presenting a 12.5 times significantly higher likelihood of acquiring HIV (95% confidence interval 4.63-33.96, P < .0001). We improved late presentation by 18.2 percentage points and prevented an estimated 58 to 70 new secondary infections. HIV screening of the general population in primary care is an effective strategy for achieving timely diagnosis and preventing new infections. Opportunistic, systematic, opt-out approaches are essential to control the HIV epidemic.

Reliability of Early Estimates of the Basic Reproduction Number of COVID-19: A Systematic Review and Meta-Analysis

OBJECTIVE

This systematic review estimated the pooled R0 for early COVID-19 outbreaks and identified the impact of study-related factors such as methods, study location and study period on the estimated R0.

METHODS

We searched electronic databases for human studies published in English between 1 December 2019 and 30 September 2020 with no restriction on country/region. Two investigators independently performed the data extraction of the studies selected for inclusion during full-text screening. The primary outcome, R0, was analysed by random-effects meta-analysis using the restricted maximum likelihood method.

RESULTS

We identified 26,425 studies through our search and included 151 articles in the systematic review, among which 81 were included in the meta-analysis. The estimates of R0 from studies included in the meta-analysis ranged from 0.4 to 12.58. The pooled R0 for COVID-19 was estimated to be 2.66 (95% CI, 2.41-2.94). The results showed heterogeneity among studies and strong evidence of a small-study effect.

CONCLUSIONS

The high heterogeneity in studies makes the use of the R0 for basic epidemic planning difficult and presents a huge problem for risk assessment and data synthesis. Consensus on the use of R0 for outbreak assessment is needed, and its use for assessing epidemic risk is not recommended.

Estimation of the Reproductive Number Trend of the Novel Coronavirus "COVID-19" in Southern Iran from July to November 2020

Background

Effective measures to control COVID-19 should be based on an understanding of its epidemiological pattern and the evaluation of its prevalence in the community. This study aimed to examine the reproductive number (R) of COVID-19 and its trend in Fars Province in southern Iran.

Methods

In this ecological study, the R trend was examined from July to November 2020. Data were collected from the daily reports of Shiraz University of Medical Sciences. R is the product of three components, namely the number of infection-producing contacts per unit time, the probability of transmission per contact, and the contagiousness period. Incidence and prevalence rates were used to calculate R. The R value was calculated in Microsoft Excel 2016.

Results

The first and second peaks of COVID-19 were observed on July 6^th and November 22^nd, respectively. The median and mean of R were 1.42 and 1.41, respectively. The highest and lowest values of R were observed on October 20^th (2.60) and September 1^st (0.46), respectively. The values of R had a slightly decreasing trend in the second half of July and November than the first half. In the second half of August and September, an increasing trend was observed than the first half. There was not much change in the second half of October.

Conclusion

The highest value of R was related to the dates when there was a higher probability of exposure to the virus, including public holidays and different occasions on which the probability of people's participation in ceremonies, communities, and gatherings was higher.

On the use of aggregated human mobility data to estimate the reproduction number

The reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

On the reproduction number in epidemics

This note provides an elementary derivation of the basic reproduction number and the effective reproduction number from the discrete Kermack-McKendrick epidemic model. The derived formulae match those derived from the continuous version of the model; however, the derivation from discrete model is a bit more intuitive. The MATLAB functions for its calculation are given. A real case example is considered and the results are compared with those obtained by the R0 and the EpiEstim software packages.

Predicting COVID-19 in very large countries: The case of Brazil

This work presents a practical proposal for estimating health system utilization for COVID-19 cases. The novel methodology developed is based on the dynamic model known as Susceptible, Infected, Removed and Dead (SIRD). The model was modified to focus on the healthcare system dynamics, rather than modeling all cases of the disease. It was tuned using data available for each Brazilian state and updated with daily figures. A figure of merit that assesses the quality of the model fit to the data was defined and used to optimize the free parameters. The parameters of an epidemiological model for the whole of Brazil, comprising a linear combination of the models for each state, were estimated considering the data available for the 26 Brazilian states. The model was validated, and strong adherence was demonstrated in most cases.

A multi-method approach to modeling COVID-19 disease dynamics in the United States

In this paper, we proposed a multi-method modeling approach to community-level spreading of COVID-19 disease. Our methodology was composed of interconnected age-stratified system dynamics models in an agent-based modeling framework that allowed for a granular examination of the scale and severity of disease spread, including metrics such as infection cases, deaths, hospitalizations, and ICU usage. Model parameters were calibrated using an optimization technique with an objective function to minimize error associated with the cumulative cases of COVID-19 during a training period between March 15 and October 31, 2020. We outlined several case studies to demonstrate the model's state- and local-level projection capabilities. We further demonstrated how model outcomes could be used to evaluate perceived levels of COVID-19 risk across different localities using a multi-criteria decision analysis framework. The model's two, three, and four week out-of-sample projection errors varied on a state-by-state basis, and generally increased as the out-of-sample projection period was extended. Additionally, the prediction error in the state-level projections was generally due to an underestimation of cases and an overestimation of deaths. The proposed modeling approach can be used as a virtual laboratory to investigate a wide range of what-if scenarios and easily adapted to future high-consequence public health threats.

Infection kinetics of Covid-19 and containment strategy

The devastating trail of Covid-19 is characterized by one of the highest mortality-to-infected ratio for a pandemic. Restricted therapeutic and early-stage vaccination still renders social exclusion through lockdown as the key containment mode.To understand the dynamics, we propose PHIRVD, a mechanistic infection propagation model that Machine Learns (Bayesian Markov Chain Monte Carlo) the evolution of six infection stages, namely healthy susceptible (H), predisposed comorbid susceptible (P), infected (I), recovered (R), herd immunized (V) and mortality (D), providing a highly reliable mortality prediction profile for 18 countries at varying stages of lockdown. Training data between 10 February to 29 June 2020, PHIRVD can accurately predict mortality profile up to November 2020, including the second wave kinetics. The model also suggests mortality-to-infection ratio as a more dynamic pandemic descriptor, substituting reproduction number. PHIRVD establishes the importance of early and prolonged but strategic lockdown to contain future relapse, complementing futuristic vaccine impact.

Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Nonparametric Methods

Containment strategies to combat epidemics such as SARS-CoV-2/COVID-19 require the availability of epidemiological parameters, e.g., the effective reproduction number. Parametric models such as the commonly used susceptible-infected-removed (SIR) compartment models fitted to observed incidence time series have limitations due to the time-dependency of the parameters. Furthermore, fatalities are delayed with respect to the counts of new cases, and the reproduction cycle leads to periodic patterns in incidence time series. Therefore, based on comprehensible nonparametric methods including time-delay correlation analyses, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented using publicly available time-series data on prevalence and fatalities. The estimates for Germany are compared with the results for seven other countries (France, Italy, the United States of America, the United Kingdom, Spain, Switzerland, and Brazil). The duration from diagnosis to death resulting from delay-time correlations turns out to be 13 days with high accuracy for Germany and Switzerland. For the other countries, the time-to-death durations have wider confidence intervals. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence. Based on the time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated. The temporal median of the instantaneous fatality-case ratio with time lag of 13 days between cases and deaths for Germany turns out to be 0.02. Time courses of asymptotic fatality-case ratios are presented for other countries, which substantially differ during the first half of the pandemic but converge to a narrow range with standard deviation 0.0057 and mean 0.024. Similar results are obtained from comparing time courses of instantaneous fatality-case ratios with optimal delay for the 8 exemplarily chosen countries. The basic reproduction number, R0, for Germany is estimated to be between 2.4 and 3.4 depending on the generation time, which is estimated based on a delay autocorrelation analysis. Resonances at about 4 days and 7 days are observed, partially attributable to weekly periodicity of sampling. The instantaneous (time-dependent) reproduction number is estimated from the incident (counts of new) cases, thus allowing us to infer the temporal behaviour of the reproduction number during the epidemic course. The time course of the reproduction number turns out to be consistent with the time-dependent per capita growth.

A non-parametric method for determining epidemiological reproduction numbers

In the spreading of infectious diseases, an important number to determine is how many other people will be infected on average by anyone who has become infected themselves. This is known as the reproduction number. This paper describes a non-parametric inverse method for extracting the full transfer function of infection, of which the reproduction number is the integral. The method is demonstrated by applying it to the timeline of hospitalisation admissions for covid-19 in the Netherlands up to May 20 2020, which is publicly available from the site of the Dutch National Institute of Public Health and the Environment (rivm.nl).

Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay

COVID-19 comes out as a sudden pandemic disease within human population. The pandemic dynamics of COVID-19 needs to be studied in detail. A pandemic model with hierarchical quarantine and time delay is proposed in this paper. In the COVID-19 case, the virus incubation period and the antibody failure will cause the time delay and reinfection, respectively, and the hierarchical quarantine strategy includes home isolation and quarantine in hospital. These factors that affect the spread of COVID-19 are well considered and analyzed in the model. The stability of the equilibrium and the nonlinear dynamics is studied as well. The threshold value τ k of the bifurcation is deduced and quantitatively analyzed. Numerical simulations are performed to establish the analytical results with suitable examples. The research reveals that the COVID-19 outbreak may recur over a period of time, which can be helpful to increase the number of tested people with or without symptoms in order to be able to early identify the clusters of infection. And before the effective vaccine is successfully developed, the hierarchical quarantine strategy is currently the best way to prevent the spread of this pandemic.

The effectiveness of quarantine and isolation determine the trend of the COVID-19 epidemic in the final phase of the current outbreak in China

OBJECTIVES

Since January 23, 2020, stringent measures for controlling the novel coronavirus epidemic have been gradually enforced and strengthened in mainland China. The detection and diagnosis have been improved, as well. However, the daily reported cases remaining at a high level make the epidemic trend prediction difficult.

METHODS

Since the traditional SEIR model does not evaluate the effectiveness of control strategies, a novel model in line with the current epidemic's process and control measures was proposed, utilizing multisource datasets including the cumulative number of reported, deceased, quarantined and suspected cases.

RESULTS

Results show that the trend of the epidemic mainly depends on quarantined and suspected cases. The predicted cumulative numbers of quarantined and suspected cases nearly reached static states, and their inflection points have already been achieved, with the epidemic's peak coming soon. The estimated effective reproduction numbers using model-free and model-based methods are decreasing, as well as new infections, while newly reported cases are increasing. Most infected cases have been quarantined or put in the suspected class, which has been ignored in existing models.

CONCLUSIONS

The uncertainty analyses reveal that the epidemic is still uncertain, and it is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China.

Spatiotemporal multi-disease transmission dynamic measure for emerging diseases: an application to dengue and zika integrated surveillance in Thailand

Background

New emerging diseases are public health concerns in which policy makers have to make decisions in the presence of enormous uncertainty. This is an important challenge in terms of emergency preparation requiring the operation of effective surveillance systems. A key concept to investigate the dynamic of infectious diseases is the basic reproduction number. However it is difficult to be applicable in real situations due to the underlying theoretical assumptions.

Methods

In this paper we propose a robust and flexible methodology for estimating disease strength varying in space and time using an alternative measure of disease transmission within the hierarchical modeling framework. The proposed measure is also extended to allow for incorporating knowledge from related diseases to enhance performance of surveillance system.

Results

A simulation was conducted to examine robustness of the proposed methodology and the simulation results demonstrate that the proposed method allows robust estimation of the disease strength across simulation scenarios. A real data example is provided of an integrative application of Dengue and Zika surveillance in Thailand. The real data example also shows that combining both diseases in an integrated analysis essentially decreases variability of model fitting.

Conclusions

The proposed methodology is robust in several simulated scenarios of spatiotemporal transmission force with computing flexibility and practical benefits. This development has potential for broad applicability as an alternative tool for integrated surveillance of emerging diseases such as Zika.

Estimation of the reproduction number and identification of periodicity for HFMD infections in northwest China

Repeated outbreaks of Hand, foot and mouth disease (HFMD) infections have been observed in recent decades and dominated by various enteroviral serotypes. In particular, enterovirus 71 (EV-A71), coxsackievirus A16 (CV-A16) and coxsackievirus A6 (CV-A6) dominated the prevalence of HFMD infections alternatively in recent years with various outbreak sizes in Baoji, a city of Shaanxi Province in Northwest China. Estimating the reproduction number for various enteroviruses serotypes in northwest China (north temperate zone) and identification of cyclicity of HFMD infections are therefore an issue of great importance for future epidemics prediction and control. The basic/effective reproduction numbers for EV-A71, CV-A16 and CV-A6 were estimated based on daily new cases in 2010, 2011 and 2018, respectively, in which the corresponding pathogen dominated the epidemic. Two different methods based on serial interval were adopted and the basic reproduction number were estimated to be in the range of (1.33, 1.46) for CV-A16, (1.20, 1.29) for EV-A71, and (1.38, 1.59) for CV-A6, respectively. The estimated daily effective reproduction numbers significantly fluctuated before June or after July but varied mildly in (0.5,2) in around June to July for three serotypes. The weekly effective reproduction number for HFMD was estimated based on weekly new cases from year 2010 to 2018, and in most years it peaked in the range of (1.6,2.0) in February to March as well as in the range of (1.0,1.2) in September to October. The wavelet analysis based on the time series of HFMD cases from 2008 to 2018 showed obvious annual and semi-annual cyclicity, while the inter-annual cycles are infeasible. In this study we found that CV-A6 shows the greatest transmission ability among these three pathogens while EV-A71 exhibits the weakest ability of transmission, and moreover, the estimated values of basic reproduction number in northwest China are lower than those in Singapore, Hongkong and Guangdong, which may be due to different climatic circumstances.

Complexity of the Basic Reproduction Number (R0)

The basic reproduction number (R₀), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R₀ is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R₀ easily misrepresented, misinterpreted, and misapplied. R₀ is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R₀ cannot be modified through vaccination campaigns. R₀ is rarely measured directly, and modeled R₀ values are dependent on model structures and assumptions. Some R₀ values reported in the scientific literature are likely obsolete. R₀ must be estimated, reported, and applied with great caution because this basic metric is far from simple.

Complexity of the Basic Reproduction Number (R0)

The basic reproduction number (R₀), also called the basic reproduction ratio or rate or the basic reproductive rate, is an epidemiologic metric used to describe the contagiousness or transmissibility of infectious agents. R₀ is affected by numerous biological, sociobehavioral, and environmental factors that govern pathogen transmission and, therefore, is usually estimated with various types of complex mathematical models, which make R₀ easily misrepresented, misinterpreted, and misapplied. R₀ is not a biological constant for a pathogen, a rate over time, or a measure of disease severity, and R₀ cannot be modified through vaccination campaigns. R₀ is rarely measured directly, and modeled R₀ values are dependent on model structures and assumptions. Some R₀ values reported in the scientific literature are likely obsolete. R₀ must be estimated, reported, and applied with great caution because this basic metric is far from simple.

Modelling the impact of correlations between condom use and sexual contact pattern on the dynamics of sexually transmitted infections

BACKGROUND

It is believed that sexually active people, i.e. people having multiple or concurrent sexual partners, are at a high risk of sexually transmitted infections (STI), but they are likely to be more aware of the risk and may exhibit greater fraction of the use of condom. The purpose of the present study is to examine the correlation between condom use and sexual contact pattern and clarify its impact on the transmission dynamics of STIs using a mathematical model.

METHODS

The definition of sexual contact pattern can be broad, but we focus on two specific aspects: (i) type of partnership (i.e. steady or casual partnership) and (ii) existence of concurrency (i.e. with single or multiple partners). Systematic review and meta-analysis of published studies are performed, analysing literature that epidemiologically examined the relationship between condom use and sexual contact pattern. Subsequently, we employ an epidemiological model and compute the reproduction number that accounts for with and without concurrency so that the corresponding coverage of condom use and its correlation with existence of concurrency can be explicitly investigated using the mathematical model. Combining the model with parameters estimated from the meta-analysis along with other assumed parameters, the impact of varying the proportion of population with multiple partners on the reproduction number is examined.

RESULTS

Based on systematic review, we show that a greater number of people used condoms during sexual contact with casual partners than with steady partners. Furthermore, people with multiple partners use condoms more frequently than people with a single partner alone. Our mathematical model revealed a positive relationship between the effective reproduction number and the proportion of people with multiple partners. Nevertheless, the association was reversed to be negative by employing a slightly greater value of the relative risk of condom use for people with multiple partners than that empirically estimated.

CONCLUSIONS

Depending on the correlation between condom use and the existence of concurrency, association between the proportion of people with multiple partners and the reproduction number can be reversed, suggesting the sexually active population is not necessary a primary target population to encourage condom use (i.e., sexually less active individuals could equivalently be a target in some cases).

Uncertainty and sensitivity analysis of the basic reproduction number of diphtheria: a case study of a Rohingya refugee camp in Bangladesh, November-December 2017

Background

A Rohingya refugee camp in Cox's Bazar, Bangladesh experienced a large-scale diphtheria epidemic in 2017. The background information of previously immune fraction among refugees cannot be explicitly estimated, and thus we conducted an uncertainty analysis of the basic reproduction number, R₀.

Methods

A renewal process model was devised to estimate the R₀ and ascertainment rate of cases, and loss of susceptible individuals was modeled as one minus the sum of initially immune fraction and the fraction naturally infected during the epidemic. To account for the uncertainty of initially immune fraction, we employed a Latin Hypercube sampling (LHS) method.

Results

R₀ ranged from 4.7 to 14.8 with the median estimate at 7.2. R₀ was positively correlated with ascertainment rates. Sensitivity analysis indicated that R₀ would become smaller with greater variance of the generation time.

Discussion

Estimated R₀ was broadly consistent with published estimate from endemic data, indicating that the vaccination coverage of 86% has to be satisfied to prevent the epidemic by means of mass vaccination. LHS was particularly useful in the setting of a refugee camp in which the background health status is poorly quantified.

The potential impact of a prophylactic vaccine for Ebola in Sierra Leone

The 2014 outbreak of Ebola virus disease (EVD) in West Africa was multinational and of an unprecedented scale primarily affecting the countries of Guinea, Liberia, and Sierra Leone. One of the qualities that makes EVD of high public concern is its potential for extremely high mortality rates (up to 90%). A prophylactic vaccine for ebolavirus (rVSV-ZEBOV) has been developed, and clinical trials show near-perfect efficacy. We have developed an ordinary differential equations model that simulates an EVD epidemic and takes into account (1) transmission through contact with infectious EVD individuals and deceased EVD bodies, (2) the heterogeneity of the risk of becoming infected with EVD, and (3) the increased survival rate of infected EVD patients due to greater access to trained healthcare providers. Using fitted parameter values that closely simulate the dynamics of the 2014 outbreak in Sierra Leone, we utilize our model to predict the potential impact of a prophylactic vaccine for the ebolavirus using various vaccination strategies including ring vaccination. Our results show that an rVSV-ZEBOV vaccination coverage as low as 40% in the general population and 95% in healthcare workers will prevent another catastrophic outbreak like the 2014 outbreak from occurring.

Frequent implementation of interventions may increase HIV infections among MSM in China

Intervention measures among men who have sex with men (MSM) are usually designed to reduce the frequency of high risk behaviors (within-community level), but unfortunately may change the contact network and consequently increase the opportunity for them to have sex with new partners (between-community level). A multi-community periodic model on complex network is proposed to study the two-side effects of interventions on HIV transmission among MSM in China, in which the wanning process of the impacts of interventions are modelled. The basic reproduction number for the multi-community periodic system is defined and calculated numerically. Based on the number of annual reported HIV/AIDS cases among MSM in China, the unknown parameters are estimated by using MCMC method and the basic reproduction number is estimated as 3.56 (95%CI [3.556, 3.568]). Our results show that strong randomness of the community-connection networks leads to more new infections and more HIV/AIDS cases. Moreover, main conclusion indicates that implementation of interventions may induce more new infections, depending on relative level of between- and within-community impacts, and the frequency of implementation of interventions. The findings can help to guide the policy maker to choose the appropriate intervention measures, and to implement the interventions with proper frequency.

Growth scaling for the early dynamics of HIV/AIDS epidemics in Brazil and the influence of socio-demographic factors

The early dynamics of an infectious disease outbreak can be affected by various factors including the transmission mode of the disease and host-specific factors. While recent works have highlighted the presence of sub-exponential growth patterns during the early phase of epidemics, empirical studies examining the contribution of different factors to early epidemic growth dynamics are lacking. Here we aim to characterize and explain the early incidence growth patterns of local HIV/AIDS epidemics in Brazil as a function of socio-demographic factors. For this purpose, we accessed annual AIDS incidence series and state-level socio-demographic variables from publicly available databases. To characterize the early growth dynamics of the HIV/AIDS epidemic, we employed the generalized-growth model to estimate with quantified uncertainty the scaling of growth parameter (p) which captures growth patterns ranging from constant incidence (p=0) to sub-exponential (0 < p < 1) and exponential growth dynamics (p=1) at three spatial scales: national, regional, and state levels. We evaluated the relationship between socio-demographic variables and epidemic growth patterns across 27 Brazilian states using mixed-effect regression analyses. We found wide variation in the early dynamics of the AIDS epidemic in Brazil, displaying sub-exponential growth patterns with the p parameter estimated substantially below 1.0. The mean p was estimated to be 0.81 at the national level, with a range of 0.72-0.85 at the regional level, and a range of 0.28-0.96 at the state level. Our findings support the notion that socio-demographic factors contribute to shaping the early growth dynamics of the epidemic at the local level. Gini index and socio-demographic index were negatively associated with the parameter p, whereas urbanicity was positively associated with p_. The results could have theoretical significance in understanding differences in growth scaling across different sexually transmitted disease systems, and have public health implications to guide control.

Characterizing the reproduction number of epidemics with early subexponential growth dynamics

Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible-infectious-removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The generalized-growth concept also provides us a compelling argument for the unexpected extinction of certain emerging disease outbreaks during the early ascending phase. Overall, our approach promotes a more reliable and data-driven characterization of the early epidemic phase, which is important for accurate estimation of the reproduction number and prediction of disease impact.

A comparative analysis of three different methods for the estimation of the basic reproduction number of dengue

The basic reproduction number, R₀, is defined as the expected number of secondary cases of a disease produced by a single infection in a completely susceptible population, and can be estimated in several ways. For example, from the stability analysis of a compartmental model; through the use of the matrix of next generation, or from the final size of an epidemic, etc. In this paper we applied the method for estimating R₀ of dengue fever from the initial growth phase of an outbreak, without assuming exponential growth of cases, a common assumption in many studies. We used three different methods of calculating R₀ to compare the techniques' details and to evaluate how these techniques estimate the value of R₀ of dengue using data from the city of Ribeirão Preto (SE of Brazil) in two outbreaks. The results of the three methods are numerically different but, when we compare them using a system of differential equations developed for modeling only the first generation time, we can observe that the methods differ little in the initial growth phase. We conclude that the methods predict that dengue will spread in the city studied and the analysis of the data shows that the estimated values of R₀ have an equal pattern overtime.

Early HAART Initiation May Not Reduce Actual Reproduction Number and Prevalence of MSM Infection: Perspectives from Coupled within- and between-Host Modelling Studies of Chinese MSM Populations

Having a thorough understanding of the infectivity of HIV, time of initiating treatment and emergence of drug resistant virus variants is crucial in mitigating HIV infection. There are many challenges to evaluating the long-term effect of the Highly Active Antiretroviral Therapy (HAART) on disease transmission at the population level. We proposed an individual based model by coupling within-host dynamics and between-host dynamics and conduct stochastic simulation in the group of men who have sex with men (MSM). The mean actual reproduction number is estimated to be 3.6320 (95% confidence interval: [3.46, 3.80]) for MSM group without treatment. Stochastic simulations show that given relatively high (low) level of drug efficacy after emergence of drug resistant variants, early initiation of treatment leads to a less (greater) actual reproduction number, lower (higher) prevalence and less (more) incidences, compared to late initiation of treatment. This implies early initiation of HAART may not always lower the actual reproduction number and prevalence of infection, depending on the level of treatment efficacy after emergence of drug resistant virus variants, frequency of high-risk behaviors and etc. This finding strongly suggests early initiation of HAART should be implemented with great care especially in the settings where the effective drugs are limited. Coupling within-host dynamics with between-host dynamics can provide critical information about impact of HAART on disease transmission and thus help to assist treatment strategy design and HIV/AIDS prevention and control.

A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks

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We introduce a generalized-growth model to characterize epidemic growth.

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The generalized-growth model capture sub-exponential and exponential epidemic growth.

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We uncovered epidemic profiles from data ranging from very slow growth to near exponential growth.

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Our findings reveal significant variation in epidemic growth patterns across outbreaks.

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Findings indicate that sub-exponential growth dynamics is a common phenomenon.

Background

A better characterization of the early growth dynamics of an epidemic is needed to dissect the important drivers of disease transmission, refine existing transmission models, and improve disease forecasts.

Materials and methods

We introduce a 2-parameter generalized-growth model to characterize the ascending phase of an outbreak and capture epidemic profiles ranging from sub-exponential to exponential growth. We test the model against empirical outbreak data representing a variety of viral pathogens in historic and contemporary populations, and provide simulations highlighting the importance of sub-exponential growth for forecasting purposes.

Results

We applied the generalized-growth model to 20 infectious disease outbreaks representing a range of transmission routes. We uncovered epidemic profiles ranging from very slow growth (p = 0.14 for the Ebola outbreak in Bomi, Liberia (2014)) to near exponential (p > 0.9 for the smallpox outbreak in Khulna (1972), and the 1918 pandemic influenza in San Francisco). The foot-and-mouth disease outbreak in Uruguay displayed a profile of slower growth while the growth pattern of the HIV/AIDS epidemic in Japan was approximately linear. The West African Ebola epidemic provided a unique opportunity to explore how growth profiles vary by geography; analysis of the largest district-level outbreaks revealed substantial growth variations (mean p = 0.59, range: 0.14–0.97). The districts of Margibi in Liberia and Bombali and Bo in Sierra Leone had near-exponential growth, while the districts of Bomi in Liberia and Kenema in Sierra Leone displayed near constant incidences.

Conclusions

Our findings reveal significant variation in epidemic growth patterns across different infectious disease outbreaks and highlights that sub-exponential growth is a common phenomenon, especially for pathogens that are not airborne. Sub-exponential growth profiles may result from heterogeneity in contact structures or risk groups, reactive behavior changes, or the early onset of interventions strategies, and consideration of “deceleration parameters” may be useful to refine existing mathematical transmission models and improve disease forecasts.

The Impact of Human Mobility on HIV Transmission in Kenya

Disease spreads as a result of people moving and coming in contact with each other. Thus the mobility patterns of individuals are crucial in understanding disease dynamics. Here we study the impact of human mobility on HIV transmission in different parts of Kenya. We build an SIR metapopulation model that incorporates the different regions within the country. We parameterise the model using census data, HIV data and mobile phone data adopted to track human mobility. We found that movement between different regions appears to have a relatively small overall effect on the total increase in HIV cases in Kenya. However, the most important consequence of movement patterns was transmission of the disease from high infection to low prevalence areas. Mobility slightly increases HIV incidence rates in regions with initially low HIV prevalences and slightly decreases incidences in regions with initially high HIV prevalence. We discuss how regional HIV models could be used in public-health planning. This paper is a first attempt to model spread of HIV using mobile phone data, and we also discuss limitations to the approach.

A Bayesian inferential approach to quantify the transmission intensity of disease outbreak

BACKGROUND

Emergence of infectious diseases like influenza pandemic (H1N1) 2009 has become great concern, which posed new challenges to the health authorities worldwide. To control these diseases various studies have been developed in the field of mathematical modelling, which is useful tool for understanding the epidemiological dynamics and their dependence on social mixing patterns.

METHOD

We have used Bayesian approach to quantify the disease outbreak through key epidemiological parameter basic reproduction number (R0), using effective contacts, defined as sum of the product of incidence cases and probability of generation time distribution. We have estimated R0 from daily case incidence data for pandemic influenza A/H1N1 2009 in India, for the initial phase.

RESULT

The estimated R0 with 95% credible interval is consistent with several other studies on the same strain. Through sensitivity analysis our study indicates that infectiousness affects the estimate of R0.

CONCLUSION

Basic reproduction number R0 provides the useful information to the public health system to do some effort in controlling the disease by using mitigation strategies like vaccination, quarantine, and so forth.

Growth patterns and scaling laws governing AIDS epidemic in Brazilian cities

Brazil holds approximately 1/3 of population living infected with AIDS (acquired immunodeficiency syndrome) in Central and South Americas, and it was also the first developing country to implement a large-scale control and intervention program against AIDS epidemic. In this scenario, we investigate the temporal evolution and current status of the AIDS epidemic in Brazil. Specifically, we analyze records of annual absolute frequency of cases for more than 5000 cities for the first 33 years of the infection in Brazil. We found that (i) the annual absolute frequencies exhibit a logistic-type growth with an exponential regime in the first few years of the AIDS spreading; (ii) the actual reproduction number decaying as a power law; (iii) the distribution of the annual absolute frequencies among cities decays with a power law behavior; (iv) the annual absolute frequencies and the number of inhabitants have an allometric relationship; (v) the temporal evolution of the annual absolute frequencies have different profile depending on the average annual absolute frequencies in the cities. These findings yield a general quantitative description of the AIDS infection dynamics in Brazil since the beginning. They also provide clues about the effectiveness of treatment and control programs against the infection, that has had a different impact depending on the number of inhabitants of cities. In this framework, our results give insights into the overall dynamics of AIDS epidemic, which may contribute to select empirically accurate models.

Estimated effects of projected climate change on the basic reproductive number of the Lyme disease vector Ixodes scapularis

BACKGROUND

The extent to which climate change may affect human health by increasing risk from vector-borne diseases has been under considerable debate.

OBJECTIVES

We quantified potential effects of future climate change on the basic reproduction number (R0) of the tick vector of Lyme disease, Ixodes scapularis, and explored their importance for Lyme disease risk, and for vector-borne diseases in general.

METHODS

We applied observed temperature data for North America and projected temperatures using regional climate models to drive an I. scapularis population model to hindcast recent, and project future, effects of climate warming on R0. Modeled R0 increases were compared with R0 ranges for pathogens and parasites associated with variations in key ecological and epidemiological factors (obtained by literature review) to assess their epidemiological importance.

RESULTS

R0 for I. scapularis in North America increased during the years 1971-2010 in spatio-temporal patterns consistent with observations. Increased temperatures due to projected climate change increased R0 by factors (2-5 times in Canada and 1.5-2 times in the United States), comparable to observed ranges of R0 for pathogens and parasites due to variations in strains, geographic locations, epidemics, host and vector densities, and control efforts.

CONCLUSIONS

Climate warming may have co-driven the emergence of Lyme disease in northeastern North America, and in the future may drive substantial disease spread into new geographic regions and increase tick-borne disease risk where climate is currently suitable. Our findings highlight the potential for climate change to have profound effects on vectors and vector-borne diseases, and the need to refocus efforts to understand these effects.

Mathematical modeling of the HIV/Kaposi's sarcoma coinfection dynamics in areas of high HIV prevalence

We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛ _k < 1. A unique endemic equilibrium exists and is locally stable whenever ℛ _k > 1. Therefore, reducing ℛ _k to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.

Modelling HIV/AIDS epidemic among men who have sex with men in China

A compartmental model with antiviral therapy was proposed to identify the important factors that influence HIV infection among gay men in China and suggest some effective control strategies. We proved that the disease will be eradicated if the reproduction number is less than one. Based on the number of annual reported HIV/AIDS among MSM we used the Markov-Chain Monte-Carlo (MCMC) simulation to estimate the unknown parameters. We estimated a mean reproduction number of 3.88 (95% CI: 3.69-4.07). The estimation results showed that there were a higher transmission rate and a lower diagnose rate among MSM than those for another high-risk population. We compared the current treatment policy and immediate therapy once people are diagnosed with HIV, and numerical studies indicated that immediate antiviral therapy would lead to few HIV new infections conditional upon relatively low infectiousness; otherwise the current treatment policy would result in low HIV new infection. Further, increasing treatment coverage rate may lead to decline in HIV new infections and be beneficial to disease control, depending on the infectiousness of the infected individuals with antiviral therapy. The finding suggested that treatment efficacy (directly affecting infectiousness), behavior changes, and interventions greatly affect HIV new infection; strengthening intensity will contribute to the disease control.

Prospects of elimination of HIV with test-and-treat strategy

Recently, there has been much debate about the prospects of eliminating HIV from high endemic countries by a test-and-treat strategy. This strategy entails regular HIV testing in the entire population and starting antiretroviral treatment immediately in all who are found to be HIV infected. We present the concept of the elimination threshold and investigate under what conditions of treatment uptake and dropout elimination of HIV is feasible. We used a deterministic model incorporating an accurate description of disease progression and variable infectivity. We derived explicit expressions for the basic reproduction number and the elimination threshold. Using estimates of exponential growth rates of HIV during the initial phase of epidemics, we investigated for which populations elimination is within reach. The concept of the elimination threshold allows an assessment of the prospects of elimination of HIV from information in the early phase of the epidemic. The relative elimination threshold quantifies prospects of elimination independently of the details of the transmission dynamics. Elimination of HIV by test-and-treat is only feasible for populations with very low reproduction numbers or if the reproduction number is lowered significantly as a result of additional interventions. Allowing low infectiousness during primary infection, the likelihood of elimination becomes somewhat higher. The elimination threshold is a powerful tool for assessing prospects of elimination from available data on epidemic growth rates of HIV. Empirical estimates of the epidemic growth rate from phylogenetic studies were used to assess the potential for elimination in specific populations.

The impact of model building on the transmission dynamics under vaccination: observable (symptom-based) versus unobservable (contagiousness-dependent) approaches

Background

The way we formulate a mathematical model of an infectious disease to capture symptomatic and asymptomatic transmission can greatly influence the likely effectiveness of vaccination in the presence of vaccine effect for preventing clinical illness. The present study aims to assess the impact of model building strategy on the epidemic threshold under vaccination.

Methodology/Principal Findings

We consider two different types of mathematical models, one based on observable variables including symptom onset and recovery from clinical illness (hereafter, the “observable model”) and the other based on unobservable information of infection event and infectiousness (the “unobservable model”). By imposing a number of modifying assumptions to the observable model, we let it mimic the unobservable model, identifying that the two models are fully consistent only when the incubation period is identical to the latent period and when there is no pre-symptomatic transmission. We also computed the reproduction numbers with and without vaccination, demonstrating that the data generating process of vaccine-induced reduction in symptomatic illness is consistent with the observable model only and examining how the effective reproduction number is differently calculated by two models.

Conclusions

To explicitly incorporate the vaccine effect in reducing the risk of symptomatic illness into the model, it is fruitful to employ a model that directly accounts for disease progression. More modeling studies based on observable epidemiological information are called for.

Linking immunological and epidemiological dynamics of HIV: the case of super-infection

In this paper, a two-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the two strains eliminate each other with the strain with the larger immunological reproduction persisting. However, on the population scale superinfection is possible, with the strain with larger immunological reproduction number super-infecting the strain with the smaller immunological reproduction number. The two models are linked through the age-since-infection structure of the epidemiological variables. In addition, the between-host transmission and the disease-induced death rate depend on the within-host viral load. The immunological reproduction numbers, the epidemiological reproduction numbers and invasion reproduction numbers are computed. Besides the disease-free equilibrium, there are two population-level strain one and strain two isolated equilibria, as well as a population-level coexistence equilibrium when both invasion reproduction numbers are greater than one. The single-strain population-level equilibria are locally asymptotically stable suggesting that in the absence of superinfection oscillations do not occur, a result contrasting previous studies of HIV age-since-infection structured models. Simulations suggest that the epidemiological reproduction number and HIV population prevalence are monotone functions of the within-host parameters with reciprocal trends. In particular, HIV medications that decrease within-host viral load also increase overall population prevalence. The effect of the immunological parameters on the population reproduction number and prevalence is more pronounced when the initial viral load is lower.

Predicting the HIV/AIDS epidemic and measuring the effect of mobility in mainland China

HIV has spread widely in mainland China, but there is significant geographic variation in the severity of the epidemic. We aimed to assess the HIV/AIDS epidemic in mainland China accurately, and address the effect of population mobility on it. Markov-Chain Monte-Carlo simulations and Latin Hypercube Sampling were used to estimate the basic reproductive ratio and its sensitivity to parameter variations. We estimated a mean reproduction number of 1.708 (95% CI 1.440-1.977). Our analysis using national surveillance data indicates that HIV-positive individuals most likely move from economically developed regions to regions with more numerous HIV cases, while mobility of AIDS patients likely flows in the opposite direction, due to the current policy that AIDS patients must return to their registered residence to receive free antiretroviral therapy. Our results based on a spatially stratified population dynamical model show increasing mobility rates of HIV/AIDS cases can have a significant effect on the number of HIV/AIDS cases per province and has the potential to decrease the overall number of HIV/AIDS cases in the country. We recommend that the community-based HIV/AIDS support and care program should be implemented by some local governments (especially in epidemically severe areas) to mitigate HIV infections in China.

Estimating the basic reproductive number from viral sequence data

Epidemiological processes leave a fingerprint in the pattern of genetic structure of virus populations. Here, we provide a new method to infer epidemiological parameters directly from viral sequence data. The method is based on phylogenetic analysis using a birth-death model (BDM) rather than the commonly used coalescent as the model for the epidemiological transmission of the pathogen. Using the BDM has the advantage that transmission and death rates are estimated independently and therefore enables for the first time the estimation of the basic reproductive number of the pathogen using only sequence data, without further assumptions like the average duration of infection. We apply the method to genetic data of the HIV-1 epidemic in Switzerland.

The failure of R0

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.