Journal of The Royal Society Interface

The reproduction number is a critical measure of the severity of an infectious disease epidemic. The generation interval, defined as the time taken by an infector to create another infection from its time of infection, is crucial for estimating the basic reproduction number. However, the generation intervals observed, realised generation intervals, change over time depending on the dynamics of the epidemic. These time varying distributions are well understood for homogeneous populations, and ca...

Epidemics generally spread through a succession of waves that reflect factors on multiple time-scales. On short time-scales, superspreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both time-scales, including time variations in individual social activity, and demonstrate how to incorporate ...

Individual-level variation in susceptibility to infection and transmissibility of infection can affect population-level dynamics in epidemic outbreaks. Prior work has incorporated independent variation in susceptibility or transmissibility of individuals into epidemic compartmental models. Here, we develop and assess a mathematical framework that includes covariation in susceptibility and transmissibility. We show that uncorrelated variation in susceptibility and transmissibility leads to an eff...

We introduce the angular reproduction number {Omega}, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number R, and generation time distribution w. Predominant approaches for tracking pathogen spread either infer R or the epidemic growth rate r. However, R is biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmissio...

The timing of transmission plays a key role in the dynamics and controllability of an epidemic. However, observing the distribution of generation times (time interval between the points of infection of an infector and infectee in a transmission pair) requires data on infection times, which are generally unknown. The timing of symptom onset is more easily observed; the generation time distribution is therefore often estimated based on the serial interval distribution (distribution of time interva...

O_LICurrent practice in the design and evaluation of epidemic control measures, including vaccination, is largely based on reproduction numbers (RNs), which represent prognostic indexes of long-term disease transmission, both in naive populations (basic RN) and in the presence of prior exposure or interventions (effective RN). A standard control objective is to establish herd immunity, e.g., by immunizing enough susceptible individuals to achieve RN<1. However, attaining this goal is not suffici...

The role of asymptomatic carriers in transmission poses challenges for control of the COVID-19 pandemic. Study of asymptomatic transmission and implications for surveillance and disease burden are ongoing, but there has been little study of the implications of asymp- tomatic transmission on dynamics of disease. We use a mathematical framework to evaluate expected effects of asymptomatic transmission on the basic reproduction number[R] 0 (i.e., the expected number of secondary cases generated by ...

Reinfection with SARS-CoV-2 can result from either waning immunity, a drift in the virus that escapes previously stimulated immunity, or both. The nature of such reinfection risks will affect the choice of control tactics and vaccines. We constructed an SIR transmission model of waning and drifting that can be fitted to cross-neutralization serological data. In this model, waning occurs in individuals who have recovered from previous infections while drifting occurs during transmission to a prev...

The basic reproductive number -- R0 -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same R0 [1-3]. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average R0 and the underlying heterogeneity. To do so, we reformu...

In this manuscript, we derive a closed form solution to the full Kermack and McKendrick integro-differential equations (Kermack and McKendrick 1927) which we call the KMES. We demonstrate the veracity of the KMES using independent data from the Covid 19 pandemic and derive many previously unknown and useful analytical expressions for characterizing and managing an epidemic. These include expressions for the viral load, the final size, the effective reproduction number, and the time to the peak i...

Early analysis of outbreaks of novel pathogens to evaluate their likely public health impact depends on fitting predictive models to data gathered and updated in real-time. Both transmission rates and the critical R0 threshold (i.e. the pathogens reproductive number) are inferred by finding the values that provide the best model fit to reported case incidence. These models and inferred results are then the basic tools used for public health planning: how many people expected to be infected, at ...

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown measures are introduced to reduce the probability of disease transmission. While in the case of uniform lockdown a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using a connected set of stocha...

Upon the development of a drug or vaccine, a successful response to a global pandemic, such as COVID-19, requires the capacity for efficient distribution at a global scale. Considering constraints on production and shipping, most existing strategies seek to maximize the outflow of therapeutics, hence optimizing for rapid dissemination. Surprisingly, we find that this intuitive approach is counterproductive. The reason is that focusing strictly on the quantity of disseminated therapeutics, such s...

Social distancing is an effective way to contain the spread of a contagious disease, particularly when facing a novel pathogen and no pharmacological interventions are available. In such cases, conventional wisdom suggests that social distancing measures should be introduced as soon as possible after the beginning of an outbreak to more effectively mitigate the spread of the disease. Using a simple epidemiological model we show that, however, there is in fact an optimal time to initiate a tempor...

To assess the long-term effect of a vaccination programme, understanding both the efficacy and the mode of action of the vaccine is crucial. The actual mode of action is difficult to infer from field trials, because of the heterogeneity of exposure to infection. Here we show an approach to determine both vaccine efficacy and the mode of action of vaccines from human challenge studies. Our approach reveals how vaccines alter an individuals susceptibility, and identifies a mixture of different mod...

The primary predictor of a disease outbreak and severity is the basic reproduction number R0, which represents the average number of secondary cases produced by introducing an infected individual into an entirely susceptible population. According to the classical SIS model, a disease with R0 less than one will eventually die out and persist if R0 is greater than one. Using the pair-approximation method, we reconstruct the classical SIS model by explicitly accounting for neighbourhood interaction...

The effective reproduction ratio r(t) of an epidemic, defined as the average number of secondary infected cases per infectious case in a population in the current state, including both susceptible and non-susceptible hosts, controls the transition between a subcritical threshold regime (r(t) < 1) and a supercritical threshold regime (r(t) > 1). While in subcritical regimes, an index infected case will cause an outbreak that will die out sooner or later, with large fluctuations observed when appr...

September 5, 2020 The SARS-CoV-2 coronavirus has proven difficult to control not only because of its high transmissibility, but because those who are infected readily spread the virus before symptoms appear, and because some infected individuals, though contagious, never exhibit symptoms. Proactive testing of asymptomatic individuals is therefore a powerful, and probably necessary, tool for preventing widespread infection in many settings. This paper explores the effectiveness of alternative te...

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most ap...

In response to the COVID19 outbreak many countries have implemented lockdown to ensure social distancing. However, long lockdowns globally affected the livelihood of millions of people resulting in subsequent unlocks that started a second wave of infection in multiple countries. Unlocking of the economies critically imposes extra burden on testing and quarantine of the infected people to keep the reproduction number (R0) <1. This, as we demonstrate, requires optimizing a cost-benefit trade-off b...