We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010–2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2016.0820

Behavioural change models for infectious disease transmission: a systematic review (2010-2015).

Airborne route and bad use of ventilation systems as non-negligible factors in SARS-CoV-2 transmission.

Background: Coronavirus Disease 2019 (COVID-19) is currently a global public health threat. Outside of China, Italy is one of the most suffering countries with the COVID-19 epidemic. It is important to predict the epidemics trend of COVID-19 epidemic in Italy to help develop public health strategies. Methods: We used time-series data of COVID-19 from Jan 22,2020 to Apr 02,2020. An infectious disease dynamic extended susceptible-infected-removed (eSIR) model, which covers the effects of different intervention measures in dissimilar periods, was applied to estimate the epidemic trend in Italy. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credible interval (CI). Hunan, with similar total number of populations in Italy, was used as a comparative item. Results: In the eSIR model, we estimated that the mean of basic reproductive number for COVID-19 was respectively 4.34 (95% CI, 3.04-6.00) in Italy and 3.16 (95% CI, 1.73-5.25) in Hunan. There would be totally 182 051 infected cases (95%CI:116 114-274 378) under the current country blockade and the endpoint would be Aug 05 in Italy. Conclusion: Italy's current strict measures can efficaciously prevent the further spread of COVID-19 and should be maintained. Necessary strict public health measures be implemented as soon as possible in other European countries with a high number of COVID-19 cases. The most effective strategy needs to be confirmed in further studies.

/pdf/extended-sir-prediction-of-the-epidemics-trend-of-covid-19-3ge1oasoyi.pdf

Extended SIR Prediction of the Epidemics Trend of COVID-19 in Italy and Compared With Hunan, China

The COVID-19 epidemic hit Italy particularly hard, yielding the implementation of strict national lockdown rules. Previous modelling studies at the national level overlooked the fact that Italy is divided into administrative regions which can independently oversee their own share of the Italian National Health Service. Here, we show that heterogeneity between regions is essential to understand the spread of the epidemic and to design effective strategies to control the disease. We model Italy as a network of regions and parameterize the model of each region on real data spanning over two months from the initial outbreak. We confirm the effectiveness at the regional level of the national lockdown strategy and propose coordinated regional interventions to prevent future national lockdowns, while avoiding saturation of the regional health systems and mitigating impact on costs. Our study and methodology can be easily extended to other levels of granularity to support policy- and decision-makers.

/pdf/a-network-model-of-italy-shows-that-intermittent-regional-gdvtzou6x5.pdf

A network model of Italy shows that intermittent regional strategies can alleviate the COVID-19 epidemic

COVID-19 is a global pandemic that has currently infected >300,000 globally. Fever and cough are the most common symptoms of the disease, and it is important to remember that the virus can even be transmitted by individuals who test positive for the disease but do not have any symptoms. Currently reported mortality rates vary because of the rapid spread of the disease and different approaches to calculating this estimate, but it is clear that the risk of death is associated with age and the presence of underlying conditions. Risk mitigation techniques (i.e., hand washing, social distancing, and self-isolation) have already been emphasized across major news outlets. It is essential that we continue these practices, as the outbreak is currently expected to last for many more months and we must be mindful of the lessons learned from past pandemics to prevent a second wave from occurring.

Novel Coronavirus COVID-19: Current Evidence and Evolving Strategies.

Background 
A striking characteristic of the past four influenza pandemic outbreaks in the United States has been the multiple waves of infections. However, the mechanisms responsible for the multiple waves of influenza or other acute infectious diseases are uncertain. Understanding these mechanisms could provide knowledge for health authorities to develop and implement prevention and control strategies.
Materials and Methods 
We exhibit five distinct mechanisms, each of which can generate two waves of infections for an acute infectious disease. The first two mechanisms capture changes in virus transmissibility and behavioral changes. The third mechanism involves population heterogeneity (e.g., demography, geography), where each wave spreads through one sub-population. The fourth mechanism is virus mutation which causes delayed susceptibility of individuals. The fifth mechanism is waning immunity. Each mechanism is incorporated into separate mathematical models, and outbreaks are then simulated. We use the models to examine the effects of the initial number of infected individuals (e.g., border control at the beginning of the outbreak) and the timing of and amount of available vaccinations.
Results 
Four models, individually or in any combination, reproduce the two waves of the 2009 H1N1 pandemic in the United States, both qualitatively and quantitatively. One model reproduces the two waves only qualitatively. All models indicate that significantly reducing or delaying the initial numbers of infected individuals would have little impact on the attack rate. Instead, this reduction or delay results in a single wave as opposed to two waves. Furthermore, four of these models also indicate that a vaccination program started earlier than October 2009 (when the H1N1 vaccine was initially distributed) could have eliminated the second wave of infection, while more vaccine available starting in October would not have eliminated the second wave.

https://mds.marshall.edu/cgi/viewcontent.cgi?article=1039&context=mathematics_faculty

A perspective on multiple waves of influenza pandemics.

Super-spreading events for infectious diseases oc- cur when some infected individuals infect more than the average number of secondary cases. Several super-spreading individuals have been identified for the 2003 outbreak of severe acute respiratory syndrome (SARS). We develop a model for super- spreading events of infectious diseases, which is based on the outbreak of SARS. Using this model we describe two methods for estimating the parameters of the model, which we demonstrate with the small-scale SARS outbreak at the Amoy Gardens, Hong Kong, and the large-scale outbreak in the entire Hong Kong Special Administrative Region. One method is based on parameters calculated for the classical susceptible - infected - removed (SIR) disease model. The second is based on parameter estimates found in the literature. Using the parameters calculated for the SIR model, our model predicts an outcome similar to that for the SIR model. On the other hand, using parameter estimates from SARS literature our model predicts a much more serious epidemic.

/pdf/modeling-super-spreading-events-for-infectious-diseases-case-13iga9a12u.pdf

Modeling Super-spreading Events for Infectious Diseases: Case Study SARS

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of new infections and deaths. Our models show that the most effective strategy to reduce infections is to provide this information as early as possible, though providing it well into the course of the outbreak can still have a significant effect. However, our models for long-term outbreaks indicate that reporting historic infection data can result in more infections than with no reporting at all. We examine three types of media influence and we illustrate the media influence with a simulated outbreak of a generic emerging infectious disease in a small city. Social distancing can never be complete; however, for a spectrum of outbreaks, we show that leaving isolation (stopping applying social distancing measures) for up to 4 hours each day has modest effect on the overall morbidity and mortality.

Get the News Out Loudly and Quickly: The Influence of the Media on Limiting Emerging Infectious Disease Outbreaks

Determining the time-dependent transmission function that exactly reproduces disease incidence data can yield useful information about disease outbreaks, including a range potential values for the recovery rate of the disease and could offer a method to test the “school year” hypothesis (seasonality) for disease transmission. Recently two procedures have been developed to recover the time-dependent transmission function, β(t), for classical disease models given the disease incidence data. We first review the β(t) recovery procedures and give the resulting formulas, using both methods, for the susceptible-infected-recovered (SIR) and susceptible-exposed-infected-recovered (SEIR) models. We present a modification of one procedure, which is then shown to be identical to the other. Second, we explore several technical issues that appear when implementing the procedure for the SIR model; these are important when generating the time-dependent transmission function for real-world disease data. Third, we extend the recovery method to heterogeneous populations modeled with a certain SIR-type model with multiple time-dependent transmission functions. Finally, we apply the β(t) recovery procedure to data from the 2002–2003 influenza season and for the six seasons from 2002–2003 through 2007–2008, for both one population class and for two age classes. We discuss the consequences of the technical conditions of the procedure applied to the influenza data. We show that the method is robust in the heterogeneous cases, producing comparable results under two different hypotheses. We perform a frequency analysis, which shows a dominant 1-year period for the multi-year influenza transmission function(s).

https://link.springer.com/content/pdf/10.1007%2Fs00285-012-0558-1.pdf

Studying the recovery procedure for the time-dependent transmission rate(s) in epidemic models

Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-invariant subset. Assume that there exists a nested family of subsets $\{\Lambda_l\}_{l \geq 1}$ that exhaust $\Lambda$, that is $\Lambda_l \subset\Lambda_{l+1}$ and $\Lambda =\bigcup_{l \geq 1} \Lambda_l$. Assume that the potential $\varphi \colon X \to \mathbb{R}$ is continuous on the closure of each $\Lambda_l$ but not necessarily continuous on $\Lambda$. We define the topological pressure of $\varphi$ on $\Lambda$. This definition is shown to have a corresponding variational principle. We apply the topological pressure and variational principle to systems with non-zero Lyapunov exponents, countable Markov shifts, and unimodal maps.

/pdf/a-variational-principle-for-discontinuous-potentials-4cqmbmh399.pdf

A variational principle for discontinuous potentials

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