Mathematical models to characterize early epidemic growth: A review

Assessing the relationship between epidemic growth scaling and epidemic size: The 2014-16 Ebola epidemic in West Africa

We assess the relationship between epidemic size and the scaling of epidemic growth of Ebola epidemics at the level of administrative areas during the 2014-16 Ebola epidemic in West Africa. For this purpose, we quantify growth scaling parameters from the ascending phase of Ebola outbreaks comprising at least 7 weeks of epidemic growth. We then study how these parameters are associated with observed epidemic sizes. For validation purposes, we also analyse two historic Ebola outbreaks. We find a high monotonic association between the scaling of epidemic growth parameter and the observed epidemic size. For example, scaling of growth parameters around 0.3-0.4, 0.4-0.6 and 0.6 are associated with epidemic sizes on the order of 350-460, 460-840 and 840-2500 cases, respectively. These results are not explained by differences in epidemic onset across affected areas. We also find the relationship between the scaling of epidemic growth parameter and the observed epidemic size to be consistent for two past Ebola outbreaks in Congo (1976) and Uganda (2000). Signature features of epidemic growth could become useful to assess the risk of observing a major epidemic outbreak, generate improved diseases forecasts and enhance the predictive power of epidemic models. Our results indicate that the epidemic growth scaling parameter is a useful indicator of epidemic size, which may have significant implications to guide control of Ebola outbreaks and possibly other infectious diseases.

Dynamics of the HIV outbreak and response in Scott County, IN, USA, 2011-15: a modelling study

BACKGROUND

In November, 2014, a cluster of HIV infections was detected among people who inject drugs in Scott County, IN, USA, with 215 HIV infections eventually attributed to the outbreak. This study examines whether earlier implementation of a public health response could have reduced the scale of the outbreak.

METHODS

In this modelling study, we derived weekly case data from the HIV outbreak in Scott County, IN, and on the uptake of HIV testing, treatment, and prevention services from publicly available reports from the US Centers for Disease Control and Prevention (CDC) and researchers from Indiana. Our primary objective was to determine if an earlier response to the outbreak could have had an effect on the number of people infected. We computed upper and lower bounds for cumulative HIV incidence by digitally extracting data from published images from a CDC study using Bio-Rad avidity incidence testing to estimate the recency of each transmission event. We constructed a generalisation of the susceptible-infectious-removed model to capture the transmission dynamics of the HIV outbreak. We computed non-parametric interval estimates of the number of individuals with an undiagnosed HIV infection, the case-finding rate per undiagnosed HIV infection, and model-based bounds for the HIV transmission rate throughout the epidemic. We used these models to assess the potential effect if the same intervention had begun at two key timepoints earlier than the actual date of the initiation of efforts to control the outbreak.

FINDINGS

The upper bound for undiagnosed HIV infections in Scott County peaked at 126 around Jan 10, 2015, over 2 months before the Governor of Indiana declared a public health emergency on March 26, 2015. Applying the observed case-finding rate scale-up to earlier intervention times suggests that an earlier public health response could have substantially reduced the total number of HIV infections (estimated to have been 183-184 infections by Aug 11, 2015). Initiation of a response on Jan 1, 2013, could have suppressed the number of infections to 56 or fewer, averting at least 127 infections; whereas an intervention on April 1, 2011, could have reduced the number of infections to ten or fewer, averting at least 173 infections.

INTERPRETATION

Early and robust surveillance efforts and case finding alone could reduce nascent epidemics. Ensuring access to HIV services and harm-reduction interventions could further reduce the likelihood of outbreaks, and substantially mitigate their severity and scope.

FUNDING

US National Institute on Drug Abuse, US National Institutes of Mental Health, US National Institutes of Health Big Data to Knowledge programme, and the US National Institutes of Health.

A dynamic vaccination strategy to suppress the recurrent epidemic outbreaks

Efficient vaccination strategy is crucial for controlling recurrent epidemic spreading on networks. In this paper, based on the analysis of real epidemic data and simulations, it's found that the risk indicator of recurrent epidemic outbreaks could be determined by the ratio of the epidemic infection rate of the year to the average infected density of the former year. According to the risk indicator, the dynamic vaccination probability of each year can be designed to suppress the epidemic outbreaks. Our simulation results show that the dynamic vaccination strategy could effectively decrease the maximal and average infected density, and meanwhile increase the time intervals of epidemic outbreaks and individuals attacked by epidemic. In addition, our results indicate that to depress the influenza outbreaks, it is not necessary to keep the vaccination probability high every year; and adjusting the vaccination probability at right time could decrease the outbreak risks with lower costs. Our findings may present a theoretical guidance for the government and the public to control the recurrent epidemic outbreaks.

Evolution-informed forecasting of seasonal influenza A (H3N2)

Interpandemic or seasonal influenza A, currently subtypes H3N2 and H1N1, exacts an enormous annual burden both in terms of human health and economic impact. Incidence prediction ahead of season remains a challenge largely because of the virus' antigenic evolution. We propose a forecasting approach that incorporates evolutionary change into a mechanistic epidemiological model. The proposed models are simple enough that their parameters can be estimated from retrospective surveillance data. These models link amino acid sequences of hemagglutinin epitopes with a transmission model for seasonal H3N2 influenza, also informed by H1N1 levels. With a monthly time series of H3N2 incidence in the United States for more than 10 years, we demonstrate the feasibility of skillful prediction for total cases ahead of season, with a tendency to underpredict monthly peak epidemic size, and an accurate real-time forecast for the 2016/2017 influenza season.

Improving early epidemiological assessment of emerging Aedes-transmitted epidemics using historical data

Model-based epidemiological assessment is useful to support decision-making at the beginning of an emerging Aedes-transmitted outbreak. However, early forecasts are generally unreliable as little information is available in the first few incidence data points. Here, we show how past Aedes-transmitted epidemics help improve these predictions. The approach was applied to the 2015-2017 Zika virus epidemics in three islands of the French West Indies, with historical data including other Aedes-transmitted diseases (chikungunya and Zika) in the same and other locations. Hierarchical models were used to build informative a priori distributions on the reproduction ratio and the reporting rates. The accuracy and sharpness of forecasts improved substantially when these a priori distributions were used in models for prediction. For example, early forecasts of final epidemic size obtained without historical information were 3.3 times too high on average (range: 0.2 to 5.8) with respect to the eventual size, but were far closer (1.1 times the real value on average, range: 0.4 to 1.5) using information on past CHIKV epidemics in the same places. Likewise, the 97.5% upper bound for maximal incidence was 15.3 times (range: 2.0 to 63.1) the actual peak incidence, and became much sharper at 2.4 times (range: 1.3 to 3.9) the actual peak incidence with informative a priori distributions. Improvements were more limited for the date of peak incidence and the total duration of the epidemic. The framework can adapt to all forecasting models at the early stages of emerging Aedes-transmitted outbreaks.

Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay

The first few disease generations of an infectious disease outbreak is the most critical phase to implement control interventions. The lack of accurate data and information during the early transmission phase hinders the application of complex compartmental models to make predictions and forecasts about important epidemic quantities. Thus, simpler models are often times better tools to understand the early dynamics of an outbreak particularly in the context of limited data. In this paper we mechanistically derive and fit a family of logistic models to spatial-temporal data of the 1905 plague epidemic in Bombay, India. We systematically compare parameter estimates, reproduction numbers, model fit, and short-term forecasts across models at different spatial resolutions. At the same time, we also assess the presence of sub-exponential growth dynamics at different spatial scales and investigate the role of spatial structure and data resolution (district level data and city level data) using simple structured models. Our results for the 1905 plague epidemic in Bombay indicates that it is possible for the growth of an epidemic in the early phase to be sub-exponential at sub-city level, while maintaining near exponential growth at an aggregated city level. We also show that the rate of movement between districts can have a significant effect on the final epidemic size.

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as [Formula: see text] but more slowly than [Formula: see text]. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.

Agent-Based Modeling in Public Health: Current Applications and Future Directions

Agent-based modeling is a computational approach in which agents with a specified set of characteristics interact with each other and with their environment according to predefined rules. We review key areas in public health where agent-based modeling has been adopted, including both communicable and noncommunicable disease, health behaviors, and social epidemiology. We also describe the main strengths and limitations of this approach for questions with public health relevance. Finally, we describe both methodologic and substantive future directions that we believe will enhance the value of agent-based modeling for public health. In particular, advances in model validation, comparisons with other causal modeling procedures, and the expansion of the models to consider comorbidity and joint influences more systematically will improve the utility of this approach to inform public health research, practice, and policy.

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.

Seasonal Influenza Forecasting in Real Time Using the Incidence Decay With Exponential Adjustment Model

Background

Seasonal influenza epidemics occur frequently. Rapid characterization of seasonal dynamics and forecasting of epidemic peaks and final sizes could help support real-time decision-making related to vaccination and other control measures. Real-time forecasting remains challenging.

Methods

We used the previously described "incidence decay with exponential adjustment" (IDEA) model, a 2-parameter phenomenological model, to evaluate the characteristics of the 2015-2016 influenza season in 4 Canadian jurisdictions: the Provinces of Alberta, Nova Scotia and Ontario, and the City of Ottawa. Model fits were updated weekly with receipt of incident virologically confirmed case counts. Best-fit models were used to project seasonal influenza peaks and epidemic final sizes.

Results

The 2015-2016 influenza season was mild and late-peaking. Parameter estimates generated through fitting were consistent in the 2 largest jurisdictions (Ontario and Alberta) and with pooled data including Nova Scotia counts (R₀ approximately 1.4 for all fits). Lower R₀ estimates were generated in Nova Scotia and Ottawa. Final size projections that made use of complete time series were accurate to within 6% of true final sizes, but final size was using pre-peak data. Projections of epidemic peaks stabilized before the true epidemic peak, but these were persistently early (~2 weeks) relative to the true peak.

Conclusions

A simple, 2-parameter influenza model provided reasonably accurate real-time projections of influenza seasonal dynamics in an atypically late, mild influenza season. Challenges are similar to those seen with more complex forecasting methodologies. Future work includes identification of seasonal characteristics associated with variability in model performance.

High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea

Background

Effective countermeasures against emerging infectious diseases require an understanding of transmission rate and basic reproduction number (R₀). R₀ for severe acute respiratory syndrome is generally considered to be >1, whereas that for Middle East respiratory syndrome (MERS) is considered to be <1. However, this does not explain the large-scale outbreaks of MERS that occurred in Kingdom of Saudi Arabia (KSA) and South Korean hospitals.

Aim: To estimate R₀ in nosocomial outbreaks of MERS.

Methods

R₀ was estimated using the incidence decay with an exponential adjustment model. The KSA and Korean outbreaks were compared using a line listing of MERS cases compiled using publicly available sources. Serial intervals to estimate R₀ were assumed to be six to eight days. Study parameters [R₀ and countermeasures (d)] were estimated by fitting a model to the cumulative incidence epidemic curves using Matlab.

Findings

The estimated R₀ in Korea was 3.9 in the best-fit model, with a serial interval of six days. The first outbreak cluster in a hospital in Pyeongtaek had an R₀ of 4.04, and the largest outbreak cluster in a hospital in Samsung had an R₀ of 5.0. Assuming a six-day serial interval, the KSA outbreaks in Jeddah and Riyadh had R₀ values of 3.9 and 1.9, respectively.

Conclusion

R₀ for the nosocomial MERS outbreaks in KSA and South Korea was estimated to be in the range of 2–5, which is significantly higher than the previous estimate of <1. Therefore, more comprehensive countermeasures are needed to address these infections.

The RAPIDD ebola forecasting challenge: Synthesis and lessons learnt

Infectious disease forecasting is gaining traction in the public health community; however, limited systematic comparisons of model performance exist. Here we present the results of a synthetic forecasting challenge inspired by the West African Ebola crisis in 2014-2015 and involving 16 international academic teams and US government agencies, and compare the predictive performance of 8 independent modeling approaches. Challenge participants were invited to predict 140 epidemiological targets across 5 different time points of 4 synthetic Ebola outbreaks, each involving different levels of interventions and "fog of war" in outbreak data made available for predictions. Prediction targets included 1-4 week-ahead case incidences, outbreak size, peak timing, and several natural history parameters. With respect to weekly case incidence targets, ensemble predictions based on a Bayesian average of the 8 participating models outperformed any individual model and did substantially better than a null auto-regressive model. There was no relationship between model complexity and prediction accuracy; however, the top performing models for short-term weekly incidence were reactive models with few parameters, fitted to a short and recent part of the outbreak. Individual model outputs and ensemble predictions improved with data accuracy and availability; by the second time point, just before the peak of the epidemic, estimates of final size were within 20% of the target. The 4th challenge scenario - mirroring an uncontrolled Ebola outbreak with substantial data reporting noise - was poorly predicted by all modeling teams. Overall, this synthetic forecasting challenge provided a deep understanding of model performance under controlled data and epidemiological conditions. We recommend such "peace time" forecasting challenges as key elements to improve coordination and inspire collaboration between modeling groups ahead of the next pandemic threat, and to assess model forecasting accuracy for a variety of known and hypothetical pathogens.

Elucidating Transmission Patterns From Internet Reports: Ebola and Middle East Respiratory Syndrome as Case Studies

The paucity of traditional epidemiological data during epidemic emergencies calls for alternative data streams to characterize the key features of an outbreak, including the nature of risky exposures, the reproduction number, and transmission heterogeneities. We illustrate the potential of Internet data streams to improve preparedness and response in outbreak situations by drawing from recent work on the 2014–2015 Ebola epidemic in West Africa and the 2015 Middle East respiratory syndrome (MERS) outbreak in South Korea. We show that Internet reports providing detailed accounts of epidemiological clusters are particularly useful to characterize time trends in the reproduction number. Moreover, exposure patterns based on Internet reports align with those derived from epidemiological surveillance data on MERS and Ebola, underscoring the importance of disease amplification in hospitals and during funeral rituals (associated with Ebola), prior to the implementation of control interventions. Finally, we discuss future developments needed to generalize Internet-based approaches to study transmission dynamics.

Reproduction numbers of infectious disease models

This primer article focuses on the basic reproduction number, ℛ 0 , for infectious diseases, and other reproduction numbers related to ℛ 0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of ℛ 0 determining whether or not the disease dies out. The next generation matrix method of calculating ℛ 0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease), cholera in humans (a disease with two transmission pathways), anthrax in animals (a disease that can be spread by dead carcasses and spores), and Zika in humans (spread by mosquitoes and sexual contacts). Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate ℛ 0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity.

Modelling community-control strategies to protect hospital resources during an influenza pandemic in Ottawa, Canada

BACKGROUND

A novel influenza virus has emerged to produce a global pandemic four times in the past one hundred years, resulting in millions of infections, hospitalizations and deaths. There is substantial uncertainty about when, where and how the next influenza pandemic will occur.

METHODS

We developed a novel mathematical model to chart the evolution of an influenza pandemic. We estimate the likely burden of future influenza pandemics through health and economic endpoints. An important component of this is the adequacy of existing hospital-resource capacity. Using a simulated population reflective of Ottawa, Canada, we model the potential impact of a future influenza pandemic under different combinations of pharmaceutical and non-pharmaceutical interventions.

RESULTS

There was substantial variation in projected pandemic impact and outcomes across intervention scenarios. In a population of 1.2 million, the illness attack rate ranged from 8.4% (all interventions) to 54.5% (no interventions); peak acute care hospital capacity ranged from 0.2% (all interventions) to 13.8% (no interventions); peak ICU capacity ranged from 1.1% (all interventions) to 90.2% (no interventions); and mortality ranged from 11 (all interventions) to 363 deaths (no interventions). Associated estimates of economic burden ranged from CAD $115 million to over $2 billion when extended mass school closure was implemented.

DISCUSSION

Children accounted for a disproportionate number of pandemic infections, particularly in household settings. Pharmaceutical interventions effectively reduced peak and total pandemic burden without affecting timing, while non-pharmaceutical measures delayed and attenuated pandemic wave progression. The timely implementation of a layered intervention bundle appeared likely to protect hospital resource adequacy in Ottawa. The adaptable nature of this model provides value in informing pandemic preparedness policy planning in situations of uncertainty, as scenarios can be updated in real time as more data become available. However-given the inherent uncertainties of model assumptions-results should be interpreted with caution.

Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov's) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014-2015 Ebola epidemic in West Africa.

Perspectives on model forecasts of the 2014-2015 Ebola epidemic in West Africa: lessons and the way forward

The unprecedented impact and modeling efforts associated with the 2014-2015 Ebola epidemic in West Africa provides a unique opportunity to document the performances and caveats of forecasting approaches used in near-real time for generating evidence and to guide policy. A number of international academic groups have developed and parameterized mathematical models of disease spread to forecast the trajectory of the outbreak. These modeling efforts often relied on limited epidemiological data to derive key transmission and severity parameters, which are needed to calibrate mechanistic models. Here, we provide a perspective on some of the challenges and lessons drawn from these efforts, focusing on (1) data availability and accuracy of early forecasts; (2) the ability of different models to capture the profile of early growth dynamics in local outbreaks and the importance of reactive behavior changes and case clustering; (3) challenges in forecasting the long-term epidemic impact very early in the outbreak; and (4) ways to move forward. We conclude that rapid availability of aggregated population-level data and detailed information on a subset of transmission chains is crucial to characterize transmission patterns, while ensemble-forecasting approaches could limit the uncertainty of any individual model. We believe that coordinated forecasting efforts, combined with rapid dissemination of disease predictions and underlying epidemiological data in shared online platforms, will be critical in optimizing the response to current and future infectious disease emergencies.

Model selection for seasonal influenza forecasting

Epidemics of seasonal influenza inflict a huge burden in temperate climes such as Melbourne (Australia) where there is also significant variability in their timing and magnitude. Particle filters combined with mechanistic transmission models for the spread of influenza have emerged as a popular method for forecasting the progression of these epidemics. Despite extensive research it is still unclear what the optimal models are for forecasting influenza, and how one even measures forecast performance.

In this paper, we present a likelihood-based method, akin to Bayes factors, for model selection when the aim is to select for predictive skill. Here, “predictive skill” is measured by the probability of the data after the forecasting date, conditional on the data from before the forecasting date. Using this method we choose an optimal model of influenza transmission to forecast the number of laboratory-confirmed cases of influenza in Melbourne in each of the 2010–15 epidemics. The basic transmission model considered has the susceptible-exposed-infectious-recovered structure with extensions allowing for the effects of absolute humidity and inhomogeneous mixing in the population. While neither of the extensions provides a significant improvement in fit to the data they do differ in terms of their predictive skill. Both measurements of absolute humidity and a sinusoidal approximation of those measurements are observed to increase the predictive skill of the forecasts, while allowing for inhomogeneous mixing reduces the skill.

We discuss how our work could be integrated into a forecasting system and how the model selection method could be used to evaluate forecasts when comparing to multiple surveillance systems providing disparate views of influenza activity.

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.

Is it growing exponentially fast? -- Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics

The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3–5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Our findings indicate that devising transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.