Insights into the evolution and emergence of a novel infectious disease

Emergence failure of early epidemics: A mathematical modeling approach

Epidemic or pathogen emergence is the phenomenon by which a poorly transmissible pathogen finds its evolutionary pathway to become a mutant that can cause an epidemic. Many mathematical models of pathogen emergence rely on branching processes. Here, we discuss pathogen emergence using Markov chains, for a more tractable analysis, generalizing previous work by Kendall and Bartlett about disease invasion. We discuss the probability of emergence failure for early epidemics, when the number of infected individuals is small and the number of the susceptible individuals is virtually unlimited. Our formalism addresses both directly transmitted and vector-borne diseases, in the cases where the original pathogen is 1) one step-mutation away from the epidemic strain, and 2) undergoing a long chain of neutral mutations that do not change the epidemiology. We obtain analytic results for the probabilities of emergence failure and two features transcending the transmission mechanism. First, the reproduction number of the original pathogen is determinant for the probability of pathogen emergence, more important than the mutation rate or the transmissibility of the emerged pathogen. Second, the probability of mutation within infected individuals must be sufficiently high for the pathogen undergoing neutral mutations to start an epidemic, the mutation threshold depending again on the basic reproduction number of the original pathogen. Finally, we discuss the parameterization of models of pathogen emergence, using SARS-CoV1 as an example of zoonotic emergence and HIV as an example for the emergence of drug resistance. We also discuss assumptions of our models and implications for epidemiology.

A practical guide to mathematical methods for estimating infectious disease outbreak risks

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants

Introduction

A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures.

Methods

Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases.

Results

We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population.

Discussion

Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments.

The effects of border control and quarantine measures on the spread of COVID-19

The rapid expansion of coronavirus disease 2019 (COVID-19) has been observed in many parts of the world. Many newly reported cases of COVID-19 during early outbreak phases have been associated with travel history from an epidemic region (identified as imported cases). For those cases without travel history, the risk of wider spreads through community contact is even higher. However, most population models assume a homogeneous infected population without considering that the imported and secondary cases contracted by the imported cases can pose different risks to community spread. We have developed an "easy-to-use" mathematical framework extending from a meta-population model embedding city-to-city connections to stratify the dynamics of transmission waves caused by imported, secondary, and others from an outbreak source region when control measures are considered. Using the cumulative number of the secondary cases, we are able to determine the probability of community spread. Using the top 10 visiting cities from Wuhan in China as an example, we first demonstrated that the arrival time and the dynamics of the outbreaks at these cities can be successfully predicted under the reproduction number R₀ = 2.92 and incubation period τ = 5.2 days. Next, we showed that although control measures can gain extra 32.5 and 44.0 days in arrival time through an intensive border control measure and a shorter time to quarantine under a low R₀ (1.4), if the R₀ is higher (2.92), only 10 extra days can be gained for each of the same measures. This suggests the importance of lowering the incidence at source regions together with infectious disease control measures in susceptible regions. The study allows us to assess the effects of border control and quarantine measures on the emergence and global spread of COVID-19 in a fully connected world using the dynamics of the secondary cases.

Epidemics in Competition: Partial Cross-Immunity

The competition between two pathogen strains during the course of an epidemic represents a fundamental step in the early evolution of emerging diseases as well as in the antigenic drift process of influenza. The outcome of the competition, however, depends not only on the epidemic properties of the two strains but also on the timing and size of the introduction, characteristics that are poorly captured by deterministic mean-field epidemic models. We describe those aspects of the competition that can be determined from the mean-field models giving the range of possible final sizes of susceptible hosts and cumulated attack rates that could be observed after an epidemic with two cross-reacting strains. In the limit where the size of the initial infection goes to zero, the possible outcomes lie on a (one dimensional) curve in the outcome space.

Evolution, human-microbe interactions, and life history plasticity

A bacterium was once a component of the ancestor of all eukaryotic cells, and much of the human genome originated in microorganisms. Today, all vertebrates harbour large communities of microorganisms (microbiota), particularly in the gut, and at least 20% of the small molecules in human blood are products of the microbiota. Changing human lifestyles and medical practices are disturbing the content and diversity of the microbiota, while simultaneously reducing our exposures to the so-called old infections and to organisms from the natural environment with which human beings co-evolved. Meanwhile, population growth is increasing the exposure of human beings to novel pathogens, particularly the crowd infections that were not part of our evolutionary history. Thus some microbes have co-evolved with human beings and play crucial roles in our physiology and metabolism, whereas others are entirely intrusive. Human metabolism is therefore a tug-of-war between managing beneficial microbes, excluding detrimental ones, and channelling as much energy as is available into other essential functions (eg, growth, maintenance, reproduction). This tug-of-war shapes the passage of each individual through life history decision nodes (eg, how fast to grow, when to mature, and how long to live).

Integrative modelling for One Health: pattern, process and participation

This paper argues for an integrative modelling approach for understanding zoonoses disease dynamics, combining process, pattern and participatory models. Each type of modelling provides important insights, but all are limited. Combining these in a '3P' approach offers the opportunity for a productive conversation between modelling efforts, contributing to a 'One Health' agenda. The aim is not to come up with a composite model, but seek synergies between perspectives, encouraging cross-disciplinary interactions. We illustrate our argument with cases from Africa, and in particular from our work on Ebola virus and Lassa fever virus. Combining process-based compartmental models with macroecological data offers a spatial perspective on potential disease impacts. However, without insights from the ground, the 'black box' of transmission dynamics, so crucial to model assumptions, may not be fully understood. We show how participatory modelling and ethnographic research of Ebola and Lassa fever can reveal social roles, unsafe practices, mobility and movement and temporal changes in livelihoods. Together with longer-term dynamics of change in societies and ecologies, all can be important in explaining disease transmission, and provide important complementary insights to other modelling efforts. An integrative modelling approach therefore can offer help to improve disease control efforts and public health responses.This article is part of the themed issue 'One Health for a changing world: zoonoses, ecosystems and human well-being'.

Quantifying the risk of pandemic influenza virus evolution by mutation and re-assortment

Large outbreaks of zoonotic influenza A virus (IAV) infections may presage an influenza pandemic. However, the likelihood that an airborne-transmissible variant evolves upon zoonotic infection or co-infection with zoonotic and seasonal IAVs remains poorly understood, as does the relative importance of accumulating mutations versus re-assortment in this process. Using discrete-time probabilistic models, we determined quantitative probability ranges that transmissible variants with 1-5 mutations and transmissible re-assortants evolve after a given number of zoonotic IAV infections. The systematic exploration of a large population of model parameter values was designed to account for uncertainty and variability in influenza virus infection, epidemiological and evolutionary processes. The models suggested that immunocompromised individuals are at high risk of generating IAV variants with pandemic potential by accumulation of mutations. Yet, both immunocompetent and immunocompromised individuals could generate high viral loads of single and double mutants, which may facilitate their onward transmission and the subsequent accumulation of additional 1-2 mutations in newly-infected individuals. This may result in the evolution of a full transmissible genotype along short chains of contact transmission. Although co-infection with zoonotic and seasonal IAVs was shown to be a rare event, it consistently resulted in high viral loads of re-assortants, which may facilitate their onward transmission among humans. The prevention or limitation of zoonotic IAV infection in immunocompromised and contact individuals, including health care workers, as well as vaccination against seasonal IAVs-limiting the risk of co-infection-should be considered fundamental tools to thwart the evolution of a novel pandemic IAV by accumulation of mutations and re-assortment.

Population viscosity suppresses disease emergence by preserving local herd immunity

Animal reservoirs for infectious diseases pose ongoing risks to human populations. In this theory of zoonoses, the introduction event that starts an epidemic is assumed to be independent of all preceding events. However, introductions are often concentrated in communities that bridge the ecological interfaces between reservoirs and the general population. In this paper, we explore how the risks of disease emergence are altered by the aggregation of introduction events within bridge communities. In viscous bridge communities, repeated introductions can elevate the local prevalence of immunity. This local herd immunity can form a barrier reducing the opportunities for disease emergence. In some situations, reducing exposure rates counterintuitively increases the emergence hazards because of off-setting reductions in local immunity. Increases in population mixing can also increase emergence hazards, even when average contact rates are conserved. Our theory of bridge communities may help guide prevention and explain historical emergence events, where disruption of stable economic, political or demographic processes reduced population viscosity at ecological interfaces.

Epidemiological feedbacks affect evolutionary emergence of pathogens

The evolutionary emergence of new pathogens via mutation poses a considerable risk to human and animal populations. Most previous studies have investigated cases where a potentially pandemic strain emerges though mutation from an initial maladapted strain (i.e., its basic reproductive ratio R0 < 1). However, an alternative (and arguably more likely) cause of novel pathogen emergence is where a "weakly adapted" strain (with R0 ≈ 1) mutates into a strongly adapted strain (with R0 ≫ 1). In this case, a proportion of the host susceptible population is removed as the first strain spreads, but the impact this feedback has on emergence of mutated strains has yet to be quantified. We produce a model of pathogen emergence that takes into account changes in the susceptible population over time and find that the ongoing depletion of susceptible individuals by the first strain has a drastic effect on the emergence probability of the mutated strain, above that assumed by just scaling the reproductive ratio. Finally, we apply our model to the documented emergence of Chikungunya virus on La Réunion Island and demonstrate that the emergence probability of the mutated strain was reduced approximately 10-fold, compared to models assuming that susceptible depletion would not affect outbreak probability. These results highlight the importance of taking population feedbacks into account when predicting disease emergence.

Introducing the outbreak threshold in epidemiology

When a pathogen is rare in a host population, there is a chance that it will die out because of stochastic effects instead of causing a major epidemic. Yet no criteria exist to determine when the pathogen increases to a risky level, from which it has a large chance of dying out, to when a major outbreak is almost certain. We introduce such an outbreak threshold (T₀), and find that for large and homogeneous host populations, in which the pathogen has a reproductive ratio R₀, on the order of 1/Log(R₀) infected individuals are needed to prevent stochastic fade-out during the early stages of an epidemic. We also show how this threshold scales with higher heterogeneity and R₀ in the host population. These results have implications for controlling emerging and re-emerging pathogens.

Infectious Disease Modeling

Infectious disease models are mathematical descriptions of the spread of infection. The majority of infectious disease models consider the spread of infection from one host to another and are sometimes grouped together as “mathematical epidemiology.” A growing body of work considers the spread of infection within an individual, often with a particular focus on interactions between the infectious agent and the host’s immune responses. Such models are sometimes grouped together as “within-host models.” Most recently, new models have been developed that consider host–pathogen interactions at two levels simultaneously: both within-host dynamics and between-host transmissions. Infectious disease models vary widely in their complexity, in their attempts to refer to data from real-life infections and in their focus on problems of an applied or more fundamental nature. This entry will focus on simpler models tightly tied to data and aimed at addressing well-defined practical problems.

Mapping populations at risk: improving spatial demographic data for infectious disease modeling and metric derivation

The use of Global Positioning Systems (GPS) and Geographical Information Systems (GIS) in disease surveys and reporting is becoming increasingly routine, enabling a better understanding of spatial epidemiology and the improvement of surveillance and control strategies. In turn, the greater availability of spatially referenced epidemiological data is driving the rapid expansion of disease mapping and spatial modeling methods, which are becoming increasingly detailed and sophisticated, with rigorous handling of uncertainties. This expansion has, however, not been matched by advancements in the development of spatial datasets of human population distribution that accompany disease maps or spatial models.Where risks are heterogeneous across population groups or space or dependent on transmission between individuals, spatial data on human population distributions and demographic structures are required to estimate infectious disease risks, burdens, and dynamics. The disease impact in terms of morbidity, mortality, and speed of spread varies substantially with demographic profiles, so that identifying the most exposed or affected populations becomes a key aspect of planning and targeting interventions. Subnational breakdowns of population counts by age and sex are routinely collected during national censuses and maintained in finer detail within microcensus data. Moreover, demographic and health surveys continue to collect representative and contemporary samples from clusters of communities in low-income countries where census data may be less detailed and not collected regularly. Together, these freely available datasets form a rich resource for quantifying and understanding the spatial variations in the sizes and distributions of those most at risk of disease in low income regions, yet at present, they remain unconnected data scattered across national statistical offices and websites.In this paper we discuss the deficiencies of existing spatial population datasets and their limitations on epidemiological analyses. We review sources of detailed, contemporary, freely available and relevant spatial demographic data focusing on low income regions where such data are often sparse and highlight the value of incorporating these through a set of examples of their application in disease studies. Moreover, the importance of acknowledging, measuring, and accounting for uncertainty in spatial demographic datasets is outlined. Finally, a strategy for building an open-access database of spatial demographic data that is tailored to epidemiological applications is put forward.

Air travel and vector-borne disease movement

Recent decades have seen substantial expansions in the global air travel network and rapid increases in traffic volumes. The effects of this are well studied in terms of the spread of directly transmitted infections, but the role of air travel in the movement of vector-borne diseases is less well understood. Increasingly however, wider reaching surveillance for vector-borne diseases and our improving abilities to map the distributions of vectors and the diseases they carry, are providing opportunities to better our understanding of the impact of increasing air travel. Here we examine global trends in the continued expansion of air transport and its impact upon epidemiology. Novel malaria and chikungunya examples are presented, detailing how geospatial data in combination with information on air traffic can be used to predict the risks of vector-borne disease importation and establishment. Finally, we describe the development of an online tool, the Vector-Borne Disease Airline Importation Risk (VBD-Air) tool, which brings together spatial data on air traffic and vector-borne disease distributions to quantify the seasonally changing risks for importation to non-endemic regions. Such a framework provides the first steps towards an ultimate goal of adaptive management based on near real time flight data and vector-borne disease surveillance.

The effects of spatial population dataset choice on estimates of population at risk of disease

Background

The spatial modeling of infectious disease distributions and dynamics is increasingly being undertaken for health services planning and disease control monitoring, implementation, and evaluation. Where risks are heterogeneous in space or dependent on person-to-person transmission, spatial data on human population distributions are required to estimate infectious disease risks, burdens, and dynamics. Several different modeled human population distribution datasets are available and widely used, but the disparities among them and the implications for enumerating disease burdens and populations at risk have not been considered systematically. Here, we quantify some of these effects using global estimates of populations at risk (PAR) of P. falciparum malaria as an example.

Methods

The recent construction of a global map of P. falciparum malaria endemicity enabled the testing of different gridded population datasets for providing estimates of PAR by endemicity class. The estimated population numbers within each class were calculated for each country using four different global gridded human population datasets: GRUMP (~1 km spatial resolution), LandScan (~1 km), UNEP Global Population Databases (~5 km), and GPW3 (~5 km). More detailed assessments of PAR variation and accuracy were conducted for three African countries where census data were available at a higher administrative-unit level than used by any of the four gridded population datasets.

Results

The estimates of PAR based on the datasets varied by more than 10 million people for some countries, even accounting for the fact that estimates of population totals made by different agencies are used to correct national totals in these datasets and can vary by more than 5% for many low-income countries. In many cases, these variations in PAR estimates comprised more than 10% of the total national population. The detailed country-level assessments suggested that none of the datasets was consistently more accurate than the others in estimating PAR. The sizes of such differences among modeled human populations were related to variations in the methods, input resolution, and date of the census data underlying each dataset. Data quality varied from country to country within the spatial population datasets.

Conclusions

Detailed, highly spatially resolved human population data are an essential resource for planning health service delivery for disease control, for the spatial modeling of epidemics, and for decision-making processes related to public health. However, our results highlight that for the low-income regions of the world where disease burden is greatest, existing datasets display substantial variations in estimated population distributions, resulting in uncertainty in disease assessments that utilize them. Increased efforts are required to gather contemporary and spatially detailed demographic data to reduce this uncertainty, particularly in Africa, and to develop population distribution modeling methods that match the rigor, sophistication, and ability to handle uncertainty of contemporary disease mapping and spread modeling. In the meantime, studies that utilize a particular spatial population dataset need to acknowledge the uncertainties inherent within them and consider how the methods and data that comprise each will affect conclusions.