Sebastian Funk

Modelling the influence of human behaviour on the spread of infectious diseases: a review

Human behaviour plays an important role in the spread of infectious diseases, and understanding the influence of behaviour on the spread of diseases can be key to improving control efforts. While behavioural responses to the spread of a disease have often been reported anecdotally, there has been relatively little systematic investigation into how behavioural changes can affect disease dynamics. Mathematical models for the spread of infectious diseases are an important tool for investigating and quantifying such effects, not least because the spread of a disease among humans is not amenable to direct experimental study. Here, we review recent efforts to incorporate human behaviour into disease models, and propose that such models can be broadly classified according to the type and source of information which individuals are assumed to base their behaviour on, and according to the assumed effects of such behaviour. We highlight recent advances as well as gaps in our understanding of the interplay between infectious disease dynamics and human behaviour, and suggest what kind of data taking efforts would be helpful in filling these gaps.

The spread of awareness and its impact on epidemic outbreaks

When a disease breaks out in a human population, changes in behavior in response to the outbreak can alter the progression of the infectious agent. In particular, people aware of a disease in their proximity can take measures to reduce their susceptibility. Even if no centralized information is provided about the presence of a disease, such awareness can arise through first-hand observation and word of mouth. To understand the effects this can have on the spread of a disease, we formulate and analyze a mathematical model for the spread of awareness in a host population, and then link this to an epidemiological model by having more informed hosts reduce their susceptibility. We find that, in a well-mixed population, this can result in a lower size of the outbreak, but does not affect the epidemic threshold. If, however, the behavioral response is treated as a local effect arising in the proximity of an outbreak, it can completely stop a disease from spreading, although only if the infection rate is below a threshold. We show that the impact of locally spreading awareness is amplified if the social network of potential infection events and the network over which individuals communicate overlap, especially so if the networks have a high level of clustering. These findings suggest that care needs to be taken both in the interpretation of disease parameters, as well as in the prediction of the fate of future outbreaks.

Modeling infectious disease dynamics in the complex landscape of global health

Mathematical modeling of infectious diseases The spread of infectious diseases can be unpredictable. With the emergence of antibiotic resistance and worrying new viruses, and with ambitious plans for global eradication of polio and the elimination of malaria, the stakes have never been higher. Anticipation and measurement of the multiple factors involved in infectious disease can be greatly assisted by mathematical methods. In particular, modeling techniques can help to compensate for imperfect knowledge, gathered from large populations and under difficult prevailing circumstances. Heesterbeek et al. review the development of mathematical models used in epidemiology and how these can be harnessed to develop successful control strategies and inform public health policy. Science, this issue 10.1126/science.aaa4339 BACKGROUND Despite many notable successes in prevention and control, infectious diseases remain an enormous threat to human and animal health. The ecological and evolutionary dynamics of pathogens play out on a wide range of interconnected temporal, organizational, and spatial scales that span hours to months, cells to ecosystems, and local to global spread. Some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or persist in environmental reservoirs. Many factors, including increasing antimicrobial resistance, human connectivity, population growth, urbanization, environmental and land-use change, as well as changing human behavior, present global challenges for prevention and control. Faced with this complexity, mathematical models offer valuable tools for understanding epidemiological patterns and for developing and evaluating evidence for decision-making in global health. ADVANCES During the past 50 years, the study of infectious disease dynamics has matured into a rich interdisciplinary field at the intersection of mathematics, epidemiology, ecology, evolutionary biology, immunology, sociology, and public health. The practical challenges range from establishing appropriate data collection to managing increasingly large volumes of information. The theoretical challenges require fundamental study of many-layered, nonlinear systems in which infections evolve and spread and where key events can be governed by unpredictable pathogen biology or human behavior. In this Review, we start with an examination of real-time outbreak response using the West African Ebola epidemic as an example. Here, the challenges range from underreporting of cases and deaths, and missing information on the impact of control measures to understanding human responses. The possibility of future zoonoses tests our ability to detect anomalous outbreaks and to estimate human-to-human transmissibility against a backdrop of ongoing zoonotic spillover while also assessing the risk of more dangerous strains evolving. Increased understanding of the dynamics of infections in food webs and ecosystems where host and nonhost species interact is key. Simultaneous multispecies infections are increasingly recognized as a notable public health burden, yet our understanding of how different species of pathogens interact within hosts is rudimentary. Pathogen genomics has become an essential tool for drawing inferences about evolution and transmission and, here but also in general, heterogeneity is the major challenge. Methods that depart from simplistic assumptions about random mixing are yielding new insights into the dynamics of transmission and control. There is rapid growth in estimation of model parameters from mismatched or incomplete data, and in contrasting model output with real-world observations. New data streams on social connectivity and behavior are being used, and combining data collected from very different sources and scales presents important challenges. All these mathematical endeavors have the potential to feed into public health policy and, indeed, an increasingly wide range of models is being used to support infectious disease control, elimination, and eradication efforts. OUTLOOK Mathematical modeling has the potential to probe the apparently intractable complexity of infectious disease dynamics. Coupled to continuous dialogue between decision-makers and the multidisciplinary infectious disease community, and by drawing on new data streams, mathematical models can lay bare mechanisms of transmission and indicate new approaches to prevention and control that help to shape national and international public health policy. Modeling for public health. Policy questions define the model’s purpose. Initial model design is based on current scientific understanding and the available relevant data. Model validation and fit to disease data may require further adaptation; sensitivity and uncertainty analysis can point to requirements for collection of additional specific data. Cycles of model testing and analysis thus lead to policy advice and improved scientific understanding. Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.

Transmission Dynamics of Zika Virus in Island Populations: A Modelling Analysis of the 2013–14 French Polynesia Outbreak

Between October 2013 and April 2014, more than 30,000 cases of Zika virus (ZIKV) disease were estimated to have attended healthcare facilities in French Polynesia. ZIKV has also been reported in Africa and Asia, and in 2015 the virus spread to South America and the Caribbean. Infection with ZIKV has been associated with neurological complications including Guillain-Barré Syndrome (GBS) and microcephaly, which led the World Health Organization to declare a Public Health Emergency of International Concern in February 2015. To better understand the transmission dynamics of ZIKV, we used a mathematical model to examine the 2013–14 outbreak on the six major archipelagos of French Polynesia. Our median estimates for the basic reproduction number ranged from 2.6–4.8, with an estimated 11.5% (95% CI: 7.32–17.9%) of total infections reported. As a result, we estimated that 94% (95% CI: 91–97%) of the total population of the six archipelagos were infected during the outbreak. Based on the demography of French Polynesia, our results imply that if ZIKV infection provides complete protection against future infection, it would take 12–20 years before there are a sufficient number of susceptible individuals for ZIKV to re-emerge, which is on the same timescale as the circulation of dengue virus serotypes in the region. Our analysis suggests that ZIKV may exhibit similar dynamics to dengue virus in island populations, with transmission characterized by large, sporadic outbreaks with a high proportion of asymptomatic or unreported cases.

Endemic disease, awareness, and local behavioural response

The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.

Potential for large outbreaks of Ebola virus disease

Highlights • We revisited data from the first known Ebola outbreak in Zaire in 1976.• Using a mathematical model, we estimated transmission rates in different settings.• Analysis suggests the person-to-person R0 was 1.34 (95% CI: 0.92–2.11).• Epidemiological conditions in 1976 could have generated a larger outbreak.

Identifying transmission cycles at the human-animal interface: the role of animal reservoirs in maintaining gambiense human african trypanosomiasis.

Many infections can be transmitted between animals and humans. The epidemiological roles of different species can vary from important reservoirs to dead-end hosts. Here, we present a method to identify transmission cycles in different combinations of species from field data. We used this method to synthesise epidemiological and ecological data from Bipindi, Cameroon, a historical focus of gambiense Human African Trypanosomiasis (HAT, sleeping sickness), a disease that has often been considered to be maintained mainly by humans. We estimated the basic reproduction number of gambiense HAT in Bipindi and evaluated the potential for transmission in the absence of human cases. We found that under the assumption of random mixing between vectors and hosts, gambiense HAT could not be maintained in this focus without the contribution of animals. This result remains robust under extensive sensitivity analysis. When using the distributions of species among habitats to estimate the amount of mixing between those species, we found indications for an independent transmission cycle in wild animals. Stochastic simulation of the system confirmed that unless vectors moved between species very rarely, reintroduction would usually occur shortly after elimination of the infection from human populations. This suggests that elimination strategies may have to be reconsidered as targeting human cases alone would be insufficient for control, and reintroduction from animal reservoirs would remain a threat. Our approach is broadly applicable and could reveal animal reservoirs critical to the control of other infectious diseases.

Temporal Changes in Ebola Transmission in Sierra Leone and Implications for Control Requirements: a Real-time Modelling Study

Background: Between August and November 2014, the incidence of Ebola virus disease (EVD) rose dramatically in several districts of Sierra Leone. As a result, the number of cases exceeded the capacity of Ebola holding and treatment centres. During December, additional beds were introduced, and incidence declined in many areas. We aimed to measure patterns of transmission in different regions, and evaluate whether bed capacity is now sufficient to meet future demand. Methods: We used a mathematical model of EVD infection to estimate how the extent of transmission in the nine worst affected districts of Sierra Leone changed between 10th August 2014 and 18th January 2015. Using the model, we forecast the number of cases that could occur until the end of March 2015, and compared bed requirements with expected future capacity. Results: We found that the reproduction number, R, defined as the average number of secondary cases generated by a typical infectious individual, declined between August and December in all districts. We estimated that R was near the crucial control threshold value of 1 in December. We further estimated that bed capacity has lagged behind demand between August and December for most districts, but as a consequence of the decline in transmission, control measures caught up with the epidemic in early 2015. Conclusions: EVD incidence has exhibited substantial temporal and geographical variation in Sierra Leone, but our results suggest that the epidemic may have now peaked in Sierra Leone, and that current bed capacity appears to be sufficient to keep the epidemic under-control in most districts.

Measuring the impact of Ebola control measures in Sierra Leone.

Significance Between June 2014 and February 2015, thousands of Ebola treatment beds were introduced in Sierra Leone, alongside other infection control measures. However, there has been criticism of the timing and focus of this response, and it remains unclear how much it contributed to curbing the 2014–2015 Ebola epidemic. Using a mathematical model, we estimated how many Ebola virus disease cases the response averted in each district of Sierra Leone. We estimated that 56,600 (95% credible interval: 48,300–84,500) Ebola cases were averted in Sierra Leone as a direct result of additional treatment beds. Moreover, the number of cases averted would have been even greater had beds been available 1 month earlier. Between September 2014 and February 2015, the number of Ebola virus disease (EVD) cases reported in Sierra Leone declined in many districts. During this period, a major international response was put in place, with thousands of treatment beds introduced alongside other infection control measures. However, assessing the impact of the response is challenging, as several factors could have influenced the decline in infections, including behavior changes and other community interventions. We developed a mathematical model of EVD transmission, and measured how transmission changed over time in the 12 districts of Sierra Leone with sustained transmission between June 2014 and February 2015. We used the model to estimate how many cases were averted as a result of the introduction of additional treatment beds in each area. Examining epidemic dynamics at the district level, we estimated that 56,600 (95% credible interval: 48,300–84,500) Ebola cases (both reported and unreported) were averted in Sierra Leone up to February 2, 2015 as a direct result of additional treatment beds being introduced. We also found that if beds had been introduced 1 month earlier, a further 12,500 cases could have been averted. Our results suggest the unprecedented local and international response led to a substantial decline in EVD transmission during 2014–2015. In particular, the introduction of beds had a direct impact on reducing EVD cases in Sierra Leone, although the effect varied considerably between districts.

Nine challenges in incorporating the dynamics of behaviour in infectious diseases models

Traditionally, the spread of infectious diseases in human populations has been modelled with static parameters. These parameters, however, can change when individuals change their behaviour. If these changes are themselves influenced by the disease dynamics, there is scope for mechanistic models of behaviour to improve our understanding of this interaction. Here, we present challenges in modelling changes in behaviour relating to disease dynamics, specifically: how to incorporate behavioural changes in models of infectious disease dynamics, how to inform measurement of relevant behaviour to parameterise such models, and how to determine the impact of behavioural changes on observed disease dynamics.