The impact of media coverage on the transmission dynamics of human influenza

Media impact research: a discrete SIR epidemic model with threshold switching and nonlinear infection forces

The media's coverage has the potential to impact human behavior and aid in the control of emergent infectious diseases. We aim to quantify and evaluate the extent to which media coverage can influence infectious disease control through a mathematical model, thus proposing a switching epidemic model that considers the effect of media coverage. The threshold strategy incorporates media influence only when the number of infected cases surpasses a specific threshold; otherwise, it is disregarded. When conducting qualitative analysis of two subsystems, focusing on the existence and stability of equilibria. Using numerical methods, the codimension-2 bifurcation analysis is adopted here to investigate the various types of equilibria within the switching system that play a vital role in pest control. On the other hand, codimension-1 bifurcation analysis reveals the existence of periodic, chaotic solutions, period-doubling bifurcations, multiple attractors and other complexities within the proposed model, which could pose challenges in disease control. Additionally, the impact of key parameters on epidemic outbreaks is analyzed, such as the initial values of susceptible and infective individuals, and discuss the potential benefits of mass media coverage in preventing emerging infectious diseases. The modeling and analytical techniques developed for threshold control strategies can be applied to other disease control efforts.

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin's maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.

Dynamics of an SEIR model with media coverage mediated nonlinear infectious force

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work, we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framework, microscopic consensus formation dynamics can be linked to macroscopic epidemic trends to trigger the collective adherence to protective measures. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.

Make it or break it: On-time vaccination intent at the time of Covid-19

On-time effective vaccination is critical to curbing a pandemic, but this is often hampered by citizens' hesitancy to get quickly vaccinated. This research concentrates on the hypothesis that, besides traditional factors in the literature, vaccination success would hinge on two dimensions: a) addressing a broader set of risk perception factors than health-related issues only, and b) securing sufficient social and institutional trust at the time of vaccination campaign launch. We test this hypothesis regarding Covid-19 vaccination preferences in six European countries and at the early stage of the pandemic by April 2020. We find that addressing the two roadblock dimensions could further boost Covid-19 vaccination coverage by 22%. The study also offers three extra innovations. The first is that the traditional segmentation logic between vaccine "acceptors", "hesitants" and "refusers" is further justified by the fact that segments have different attitudes: refusers care less about health issues than they are worried about family tensions and finance (dimension 1 of our hypothesis). In contrast, hesitants are the battlefield for more transparency by media and government actions (dimension 2 of our hypothesis). The second added value is that we extend our hypothesis testing with a supervised non-parametric machine learning technique (Random Forests). Again, consistent with our hypothesis, this method picks up higher-order interaction between risk and trust variables that strongly predict on-time vaccination intent. We finally explicitly adjust survey responses to account for possible reporting bias. Among others, vaccine-reluctant citizens may under-report their limited will to get vaccinated.

Impact of public sentiments on the transmission of COVID-19 across a geographical gradient

COVID-19 is a respiratory disease caused by a recently discovered, novel coronavirus, SARS-COV-2. The disease has led to over 81 million confirmed cases of COVID-19, with close to two million deaths. In the current social climate, the risk of COVID-19 infection is driven by individual and public perception of risk and sentiments. A number of factors influences public perception, including an individual's belief system, prior knowledge about a disease and information about a disease. In this article, we develop a model for COVID-19 using a system of ordinary differential equations following the natural history of the infection. The model uniquely incorporates social behavioral aspects such as quarantine and quarantine violation. The model is further driven by people's sentiments (positive and negative) which accounts for the influence of disinformation. People's sentiments were obtained by parsing through and analyzing COVID-19 related tweets from Twitter, a social media platform across six countries. Our results show that our model incorporating public sentiments is able to capture the trend in the trajectory of the epidemic curve of the reported cases. Furthermore, our results show that positive public sentiments reduce disease burden in the community. Our results also show that quarantine violation and early discharge of the infected population amplifies the disease burden on the community. Hence, it is important to account for public sentiment and individual social behavior in epidemic models developed to study diseases like COVID-19.

Sliding dynamics and bifurcations of a human influenza system under logistic source and broken line control strategy

This paper proposes a non-smooth human influenza model with logistic source to describe the impact on media coverage and quarantine of susceptible populations of the human influenza transmission process. First, we choose two thresholds $ I_{T} $ and $ S_{T} $ as a broken line control strategy: Once the number of infected people exceeds $ I_{T} $, the media influence comes into play, and when the number of susceptible individuals is greater than $ S_{T} $, the control by quarantine of susceptible individuals is open. Furthermore, by choosing different thresholds $ I_{T} $ and $ S_{T} $ and using Filippov theory, we study the dynamic behavior of the Filippov model with respect to all possible equilibria. It is shown that the Filippov system tends to the pseudo-equilibrium on sliding mode domain or one endemic equilibrium or bistability endemic equilibria under some conditions. The regular/virtulal equilibrium bifurcations are also given. Lastly, numerical simulation results show that choosing appropriate threshold values can prevent the outbreak of influenza, which implies media coverage and quarantine of susceptible individuals can effectively restrain the transmission of influenza. The non-smooth system with logistic source can provide some new insights for the prevention and control of human influenza.

Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection

Infectious diseases have remained one of humanity's biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the co-dynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable when R C < 1 , whereas the influenza-only model, is locally asymptotically stable when R F < 1 . Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19-influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and within-hosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.

Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases

The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent.

Emotional profiling and cognitive networks unravel how mainstream and alternative press framed AstraZeneca, Pfizer and COVID-19 vaccination campaigns

COVID-19 vaccines have been largely debated by the press. To understand how mainstream and alternative media debated vaccines, we introduce a paradigm reconstructing time-evolving narrative frames via cognitive networks and natural language processing. We study Italian news articles massively re-shared on Facebook/Twitter (up to 5 million times), covering 5745 vaccine-related news from 17 news outlets over 8 months. We find consistently high trust/anticipation and low disgust in the way mainstream sources framed “vaccine/vaccino”. These emotions were crucially missing in alternative outlets. News titles from alternative sources framed “AstraZeneca” with sadness, absent in mainstream titles. Initially, mainstream news linked mostly “Pfizer” with side effects (e.g. “allergy”, “reaction”, “fever”). With the temporary suspension of “AstraZeneca”, negative associations shifted: Mainstream titles prominently linked “AstraZeneca” with side effects, while “Pfizer” underwent a positive valence shift, linked to its higher efficacy. Simultaneously, thrombosis and fearful conceptual associations entered the frame of vaccines, while death changed context, i.e. rather than hopefully preventing deaths, vaccines could be reported as potential causes of death, increasing fear. Our findings expose crucial aspects of the emotional narratives around COVID-19 vaccines adopted by the press, highlighting the need to understand how alternative and mainstream media report vaccination news.

Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.

FOMO (fate of online media only) in infectious disease modeling: a review of compartmental models

Mathematical models played in a major role in guiding policy decisions during the COVID-19 pandemic. These models while focusing on the spread and containment of the disease, largely ignored the impact of media on the disease transmission. Media plays a major role in shaping opinions, attitudes and perspectives and as the number of people online increases, online media are fast becoming a major source for news and health related information and advice. Consequently, they may influence behavior and in due course disease dynamics. Unlike traditional media, online media are themselves driven and influenced by their users and thus have unique features. The main techniques used to incorporate online media mathematically into compartmental models, with particular reference to the ongoing COVID-19 pandemic are reviewed. In doing so, features specific to online media that have yet to be fully integrated into compartmental models such as misinformation, different time scales with regards to disease transmission and information, time delays, information super spreaders, the predatory nature of online media and other factors are identified together with recommendations for their incorporation.

The Effect of Media in Mitigating Epidemic Outbreaks: The Sliding Mode Control Approach

Ever since the World Health Organization gave the name COVID-19 to the coronavirus pneumonia disease, much of the world has been severely impact by the pandemic socially and economically. In this paper, the mathematical modeling and stability analyses in terms of the susceptible–exposed–infected–removed (SEIR) model with a nonlinear incidence rate, along with media interaction effects, are presented. The sliding mode control methodology is used to design a robust closed loop control of the epidemiological system, where the property of symmetry in the Lyapunov function plays a vital role in achieving the global asymptotic stability in the output. Two policies are considered: the first considers only the governmental interaction, the second considers only the vaccination policy. Numerical simulations of the control algorithms are then evaluated.

Modeling the impacts of awareness and limited medical resources on the epidemic size of a multi-group SIR epidemic model

The pharmaceutical interventions of emerging infectious diseases are constrained by the available medical resources such as drugs, vaccines, hospital beds, isolation places and the efficiency of the treatment. The awareness of the population also plays an important role in reducing contacts and consequently, reducing the disease transmission rate. In this paper, we propose a multi-group Susceptible, Infected and Recovered (SIR) epidemic model incorporating the awareness of population and the saturated treatment function that describes the effects of the availability of medical resources for treatment. We assume that the treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. We calculate the basic reproduction number [Formula: see text] in the term of the awareness parameter using the next generation approach. We determine the local and global stabilities of equilibrium (disease free equilibrium and endemic equilibrium) in terms of [Formula: see text] and the availability of medical resources for treatment. We obtain that backward bifurcation occurs at [Formula: see text] along with the existence of multiple endemic equilibria when [Formula: see text] Further, we consider the special case with a single group epidemic system and ensure the existence of multiple endemic equilibria. We showed a necessary condition on the parameter related to the availability of medical resources when backward bifurcation occurs. This situation indicates that reducing the basic reproduction number below unity is not sufficient to remove the disease when the medical resources for treatment are scarce. We used numerical simulations to support and counterpart our theoretical results and discussed the impacts of the awareness of susceptible population and availability of medical resources for treatment in each group, on the epidemic size of each group. Our findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease (to reduce the prevalence of infection) and the eradication of disease also depends on initial population sizes. More importantly, it is also obtained that sufficient medical resources for every group are required to eradicate the disease from an entire population.

Pattern Formation in Epidemic Model with Media Coverage

In this article, a spatial epidemic model with media coverage is studied. By both mathematical analysis and numerical simulation, we found that there are some typical dynamics of population density such as the formation of the hole, stripe, spot, coexistence of hole and stripe or spot and stripe. The obtained results exhibit that parameters describing media coverage have a significant influence on the spatial pattern of the disease. More specifically, the sequential change in behaviour of the spatial pattern is observed as the parameter that accounts for media coverage increases. These changes analogous to the effect due to the rise in the basic reproduction number. The results presented in this article thus can be applied to any particular disease with some modification to study the effects of media coverage on disease dynamics. The model is although simple but the idea can be well extended to other complex problems.

Release and Demand of Public Health Information in Social Media During the Outbreak of COVID-19 in China

Information release is a key to the macro-economy during the outbreak of the Coronavirus Diosease-2019 (COVID-19). To explore the relationship between information supply by the government and public information demand in the pandemic, this study collected over 4,000 posts published on the most popular social media platform, i.e., WeChat. Many approaches, such as text mining, are employed to explore the information at different stages during the pandemic. According to the results, the government attached great importance to the information related to the pandemic. The main topics of information released by the government included the latest situation of the pandemic, announcements by the State Council, and prevention policies for COVID-19. Information mismatch between the public and Chinese governments contributed to the economic depression caused by the pandemic. Specifically, the topics of “the latest situation” and “popular scientific knowledge regarding the pandemic” have gained the most attention of the public. The information demand of the public has changed from the pandemic itself to the recovery of social life and industrial activities after the authority announced the control of the pandemic. However, during the recession phase, the information demand has shifted to asymptomatic infections and global pandemic trends. By contrast, some of the main topics provided by the government, such as “How beautiful you are,” were excessive because the public demand is insufficient. Therefore, severe mismatches existed between information release of the government and public information demand during the pandemic, which impeded the recovery of the economy. The results in this study provide strategical suggestions of information release and opinion guidance for the authorities.

Global dynamics for a Filippov system with media effects

In the process of spreading infectious diseases, the media accelerates the dissemination of information, and people have a deeper understanding of the disease, which will significantly change their behavior and reduce the disease transmission; it is very beneficial for people to prevent and control diseases effectively. We propose a Filippov epidemic model with nonlinear incidence to describe media's influence in the epidemic transmission process. Our proposed model extends existing models by introducing a threshold strategy to describe the effects of media coverage once the number of infected individuals exceeds a threshold. Meanwhile, we perform the stability of the equilibriua, boundary equilibrium bifurcation, and global dynamics. The system shows complex dynamical behaviors and eventually stabilizes at the equilibrium points of the subsystem or pseudo equilibrium. In addition, numerical simulation results show that choosing appropriate thresholds and control intensity can stop infectious disease outbreaks, and media coverage can reduce the burden of disease outbreaks and shorten the duration of disease eruptions.

Social media effectiveness as a humanitarian response to mitigate influenza epidemic and COVID-19 pandemic

Influenza and COVID-19 are infectious diseases with significant burdens. Information and awareness on preventative techniques can be spread through the use of social media, which has become an increasingly utilized tool in recent years. This study developed a dynamic transmission model to investigate the impact of social media, particularly tweets via the social networking platform, Twitter on the number of influenza and COVID-19 cases of infection and deaths. We modified the traditional Susceptible-Exposed-Infectious-Recovered (SEIR-V) model with an additional social media component, in order to increase the accuracy of transmission dynamics and gain insight on whether social media is a beneficial behavioral intervention for these infectious diseases. The analysis found that social media has a positive effect in mitigating the spread of contagious disease in terms of peak time, peak magnitude, total infected, and total death; and the results also showed that social media's effect has a non-linear relationship with the reproduction number R 0 and it will be amplified when a vaccine is available. The findings indicate that social media is an integral part in the humanitarian logistics of pandemic and emergency preparedness, and contributes to the literature by informing best practices in the response to similar disasters.

Discrete epidemic modelling of COVID-19 transmission in Shaanxi Province with media reporting and imported cases

The large-scale infection of COVID-19 has led to a significant impact on lives and economies around the world and has had considerable impact on global public health. Social distancing, mask wearing and contact tracing have contributed to containing or at least mitigating the outbreak, but how public awareness influences the effectiveness and efficiency of such approaches remains unclear. In this study, we developed a discrete compartment dynamic model to mimic and explore how media reporting and the strengthening containment strategies can help curb the spread of COVID-19 using Shaanxi Province, China, as a case study. The targeted model is parameterized based on multi-source data, including the cumulative number of confirmed cases, recovered individuals, the daily number of media-reporting items and the imported cases from the rest of China outside Shaanxi from January 23 to April 11, 2020. We carried out a sensitivity analysis to investigate the effect of media reporting and imported cases on transmission. The results revealed that reducing the intensity of media reporting, which would result in a significant increasing of the contact rate and a sizable decreasing of the contact-tracing rate, could aggravate the outbreak severity by increasing the cumulative number of confirmed cases. It also demonstrated that diminishing the imported cases could alleviate the outbreak severity by reducing the length of the epidemic and the final size of the confirmed cases; conversely, delaying implementation of lockdown strategies could prolong the length of the epidemic and magnify the final size. These findings suggest that strengthening media coverage and timely implementing of lockdown measures can significantly reduce infection.

Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India

In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

ROLE OF MEDIA COVERAGE IN MITIGATING AN EPIDEMIC OUTBREAK: AN OPTIMAL CONTROL MODEL

Flu is an acute respiratory infection caused by the influenza virus. The outbreak usually occurs every year in temperate region during the fall and winter seasons, but it is present year-round in tropics. Perceived risk of infection, affordability and lack of awareness among the population results in a low level of vaccination coverage. To control disease transmission and promote vaccination, public health officials use media coverage to spread awareness on vaccine safety, vaccine coverage, disease prevalence in the population through public health websites, advertisements, and other social media web pages. Media coverage acts as an incentive as it helps to decrease overall transmission potential and also at the same time increases the vaccination coverage in the population. Since the public health department has a limited budget, it needs to make optimum allocation of its effort to reduce the total cost of infection. Our paper investigates the effect of media coverage using SIR model of disease transmission. We look at three possible functional relationships — linear, exponential, and hyperbolic — the way media coverage may affect the disease transmission and vaccination rate. We derive necessary conditions of optimal solution using Optimal Control Theory and Pontryagin Maximum Principle (PMP) to minimize the total cost for infection. Analysis of our paper demonstrates that the cost of optimal management is four times less than the cost of constant control effort, and putting more effort into reducing transmission is optimal rather than an effort to increase vaccination at the beginning of the outbreak. Analysis of the role of media coverage under three different scenarios may help in formulating policies for public health programs in mitigating the influenza outbreak.

Citizen journalism reduces the credibility deficit of authoritarian government in risk communication amid COVID-19 outbreaks

During the outbreak of an epidemic, the success in risk communications to make the public comply with disease preventive measures depends on the public’s trust in the government. In this study, we aim to understand how media audiences update their trust in the government during the COVID-19 outbreak depending on the information they received. We conducted an online survey experiment in February 2020 in Hong Kong (n = 1,016) in which respondents were randomly provided with a government press release and an endorsement either from an official or a non-official source. This study shows that the information from a non-official source enhances the credibility of official government messages. Our findings imply that dictators can actually “borrow credibility” from their citizen journalists and even nondemocratic leaders can make themselves more trustworthy to potential dissenters through citizen journalism. Allowing information flow from non-official sources can be a practical measure for governments to address the problem of a credibility deficit during a pandemic.

Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

A stochastic vaccinated epidemic model incorporating Lévy processes with a general awareness-induced incidence

In this paper, we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Lévy noise. First, we show that this model has a unique global positive solution. Therefore, we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points. Furthermore, when [Formula: see text], we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Lévy noise is null. Finally, we present some examples to illustrate the analytical results by numerical simulations.

The influence of awareness campaigns on the spread of an infectious disease: a qualitative analysis of a fractional epidemic model

Mass-media coverage is one of the most widely used government strategies on influencing public opinion in times of crisis. Awareness campaigns are highly influential tools to expand healthy behavior practices among individuals during epidemics and pandemics. Mathematical modeling has become an important tool in analyzing the effects of media awareness on the spread of infectious diseases. In this paper, a fractional-order epidemic model incorporating media coverage is presented and analyzed. The problem is formulated using susceptible, infectious and recovered compartmental model. A long-term memory effect modeled by a Caputo fractional derivative is included in each compartment to describe the evolution related to the individuals’ experiences. The well-posedness of the model is investigated in terms of global existence, positivity, and boundedness of solutions. Moreover, the disease-free equilibrium and the endemic equilibrium points are given alongside their local stabilities. By constructing suitable Lyapunov functions, the global stability of the disease-free and endemic equilibria is proven according to the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0. Finally, numerical simulations are performed to support our analytical findings. It was found out that the long-term memory has no effect on the stability of the equilibrium points. However, for increased values of the fractional derivative order parameter, each solution reaches its equilibrium state more rapidly. Furthermore, it was observed that an increase of the media awareness parameter, decreases the magnitude of infected individuals, and consequently, the height of the epidemic peak.

Stochastic analysis of COVID-19 by a SEIR model with Lévy noise

We propose a Lévy noise-driven susceptible-exposed-infected-recovered model incorporating media coverage to analyze the outbreak of COVID-19. We conduct a theoretical analysis of the stochastic model by the suitable Lyapunov function, including the existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium; we deduce a stochastic basic reproduction number R₀ ^s for the extinction of disease, that is, if R₀ ^s≤1, the disease will go to extinction. Particularly, we fit the data from Brazil to predict the trend of the epidemic. Our main findings include the following: (i) stochastic perturbation may affect the dynamic behavior of the disease, and larger noise will be more beneficial to control its spread; (ii) strengthening social isolation, increasing the cure rate and media coverage can effectively control the spread of disease. Our results support the feasible ways of containing the outbreak of the epidemic.

Joint impacts of media, vaccination and treatment on an epidemic Filippov model with application to COVID-19

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

Numerical study of fractional order COVID-19 pandemic transmission model in context of ABO blood group

The worldwide association of health (WHO) has stated that COVID-19 (the novel coronavirus disease-2019) as a pandemic. Here, the common SEIR model is generalized in order to show the dynamics of COVID-19 transmission taking into account the ABO blood group of the infected people. Fractional order Caputo derivative are used in the proposed model. Our study is guided by the results that have been obtained by Chen J, Fan H, Zhang L, et al. from three unique medical clinics in Wuhan and Shenzhen, China. In this study, the feasibility region of the proposed model are calculated plus the points of equilibrium. Also, the equilibrium points stability is examined. A unique solution existence for the proposed paradigm is proved via utilizing the fixed point theory with regards to Caputo fractional derivative. Numerical experiments of the proposed paradigm is done and we show its sensitivity to the fractional order.

Cost and social distancing dynamics in a mathematical model of COVID-19 with application to Ontario, Canada

A mathematical model of COVID-19 is presented where the decision to increase or decrease social distancing is modelled dynamically as a function of the measured active and total cases as well as the perceived cost of isolating. Along with the cost of isolation, we define an overburden healthcare cost and a total cost. We explore these costs by adjusting parameters that could change with policy decisions. We observe that two disease prevention practices, namely increasing isolation activity and increasing incentive to isolate do not always lead to optimal health outcomes. We demonstrate that this is due to the fatigue and cost of isolation. We further demonstrate that an increase in the number of lock-downs, each of shorter duration can lead to minimal costs. Our results are compared with case data in Ontario, Canada from March to August 2020 and details of expanding the results to other regions are presented.

Dynamics of a stage-structured SI model for food adulteration with media-induced response function

In this work, an eco-epidemic predator-prey model with media-induced response function for the interaction of humans with adulterated food is developed and studied. The human population is divided into two main compartments, namely, susceptible and infected. This system has three equilibria; trivial, disease-free and endemic. The trivial equilibrium is forever an unstable saddle position, while the disease-free state is locally asymptotically stable under a threshold of delay parameter τ as well as R 0 < 1 . The sufficient conditions for the local stability of the endemic equilibrium point are further explored when min { R 0 , R 0 ∗ } > 1 . The conditions for the occurrence of the stability switching are also determined by taking infection delay time as a critical parameter, which concludes that the delay can produce instability and small amplitude oscillations of population masses via Hopf bifurcations. Further, we study the stability and direction of the Hopf bifurcations using the center manifold argument. Furthermore, some numerical simulations are conducted to validate our analytical findings and discuss their biological inferences. Finally, the normalized forward sensitivity index is used to perform the sensitivity analysis of R 0 and R 0 ∗ .

Dissemination and Refutation of Rumors During the COVID-19 Outbreak in China: Infodemiology Study

Background

During the outbreak of COVID-19, numerous rumors emerged on the internet in China and caused confusion among the public. However, the characteristics of these rumors in different phases of the epidemic have not been studied in depth, and the official responses to the rumors have not been systematically evaluated.

Objective

The aims of this study were to evaluate the rumor epidemic and official responses during the COVID-19 outbreak in China and to provide a scientific basis for effective information communication in future public health crises.

Methods

Data on internet rumors related to COVID-19 were collected via the Sina Weibo Official Account to Refute Rumors between January 20 and April 8, 2020, extracted, and analyzed. The data were divided into five periods according to the key events and disease epidemic. Different classifications of rumors were described and compared over the five periods. The trends of the epidemic and the focus of the public at different stages were plotted, and correlation analysis between the number of rumors and the number of COVID-19 cases was performed. The geographic distributions of the sources and refuters of the rumors were graphed, and analyses of the most frequently appearing words in the rumors were applied to reveal hotspots of the rumors.

Results

A total of 1943 rumors were retrieved. The median of the response interval between publication and debunking of the rumors was 1 day (IQR 1-2). Rumors in text format accounted for the majority of the 1943 rumors (n=1241, 63.9%); chat tools, particularly WeChat (n=1386, 71.3%), were the most common platform for initial publishing of the rumors (n=1412, 72.7%). In addition to text rumors, Weibo and web pages were more likely to be platforms for rumors released in multimedia formats or in a combination of formats, respectively. Local agencies played a large role in dispelling rumors among social media platforms (1537/1943, 79.1%). There were significant differences in the formats and origins of rumors over the five periods (P<.001). Hubei Province accounted for most of the country’s confirmed rumors. Beijing and Wuhan City were the main centers for debunking of disinformation. The words most frequently included in the core messages of the rumors varied by period, indicating shifting in the public’s concern.

Conclusions

Chat tools, particularly WeChat, became the major sources of rumors during the COVID-19 outbreak in China, indicating a requirement to establish rumor monitoring and refuting mechanisms on these platforms. Moreover, targeted policy adjustments and timely release of official information are needed in different phases of the outbreak.

Study on an SIHRS Model of COVID-19 Pandemic With Impulse and Time Delay Under Media Coverage

Media coverage plays an important role in prevention and control the spread of COVID-19 during the pandemic. In this paper, an SIHRS model of COVID-19 pandemic with impulse and time delay under media coverage is established. The positive and negative emotions of public are considered by the impact of confirmed cases and medical resources. In order to restrain the negative information of public, the factor of policies and regulations with impulse and time delay is introduced. Furthermore, the system model is simulated and verified by the reported data of COVID-19 pandemic in Wuhan. The main results are as follows: (1) When the implementation rate of the negative information generated by the confirmed cases gradually reduced to 0.4 times, the cumulative confirmed cases will be significantly reduced to about 37000, indicating that the popularization of pandemic related media information should be broad; (2) When the implementation rate affected by the amount of policies and regulations information gradually increases to 3 times, the cumulative confirmed cases will be significantly reduced to about 28000, indicating that the policies and regulations information should be continuously and incrementally reported; (3) When the inhibition rate of policies and regulation information on negative information gradually increases to 3 times, the cumulative confirmed cases will also be significantly reduced to about 27000 cases, indicating that the targeted policies and regulations information has a significant impact on inhibiting the corresponding negative emotions.

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

In this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

Global dynamics for a Filippov epidemic system with imperfect vaccination

Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formulated Filippov system, we examine the sliding mode dynamics, the boundary equilibrium bifurcations, and the global dynamics. Our main results show that it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depend on the threshold value and other parameter values. The global stability of the disease-free equilibrium or pseudo-equilibrium reveals that we may eradicate the disease or maintain the number of infected individuals at a previously given value. Further, the bi-stability and tri-stability imply that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. This emphasizes the importance of threshold policy and challenges in the control of infectious diseases if without perfect vaccines.

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

We present a mathematical model for the transmission of COVID-19 by the Caputo fractional-order derivative. We calculate the equilibrium points and the reproduction number for the model and obtain the region of the feasibility of system. By fixed point theory, we prove the existence of a unique solution. Using the generalized Adams-Bashforth-Moulton method, we solve the system and obtain the approximate solutions. We present a numerical simulation for the transmission of COVID-19 in the world, and in this simulation, the reproduction number is obtained as R 0 = 1 : 610007996 , which shows that the epidemic continues.

Optimal Management of Public Perceptions During A Flu Outbreak: A Game-Theoretic Perspective

Public perceptions and sentiments play a crucial role in the success of vaccine uptake in the community. While vaccines have proven to be the best preventive method to combat the flu, the attitude and knowledge about vaccines are a major hindrance to higher uptake in most of the countries. The yearly coverage, especially in the vulnerable groups in the population, often remains below the herd immunity level despite the Flu Awareness Campaign organized by WHO every year worldwide. This brings immense challenges to the nation's public health protection agency for strategic decision-making in controlling the flu outbreak every year. To understand the impact of public perceptions and vaccination decisions while designing optimal immunization policy, we model the individual decision-making as a two-strategy pairwise contest game, where pay-off is considered as a function of public health effort for the campaign. We use Pontryagin's maximum principle to identify the best possible strategy for public health to implement vaccination and reduce infection at a minimum cost. Our optimal analysis shows that the cost of public health initiatives is qualitatively and quantitatively different under different public perceptions and attitudes towards vaccinations. When individual risk perception evolves with vaccine uptake or disease induced death, our model demonstrates a feed-forward mechanism in the dynamics of vaccination and exhibits an increase in vaccine uptake. Using numerical simulation, we also observe that the optimal cost can be minimized by putting the effort in the beginning and later part of the outbreak rather than during the peak. It confers that public health efforts towards disseminating disease severity or actual vaccination risk might accelerate the vaccination coverage and mitigate the infection faster.

Collective Response to Media Coverage of the COVID-19 Pandemic on Reddit and Wikipedia: Mixed-Methods Analysis

BACKGROUND

The exposure and consumption of information during epidemic outbreaks may alter people's risk perception and trigger behavioral changes, which can ultimately affect the evolution of the disease. It is thus of utmost importance to map the dissemination of information by mainstream media outlets and the public response to this information. However, our understanding of this exposure-response dynamic during the COVID-19 pandemic is still limited.

OBJECTIVE

The goal of this study is to characterize the media coverage and collective internet response to the COVID-19 pandemic in four countries: Italy, the United Kingdom, the United States, and Canada.

METHODS

We collected a heterogeneous data set including 227,768 web-based news articles and 13,448 YouTube videos published by mainstream media outlets, 107,898 user posts and 3,829,309 comments on the social media platform Reddit, and 278,456,892 views of COVID-19-related Wikipedia pages. To analyze the relationship between media coverage, epidemic progression, and users' collective web-based response, we considered a linear regression model that predicts the public response for each country given the amount of news exposure. We also applied topic modelling to the data set using nonnegative matrix factorization.

RESULTS

Our results show that public attention, quantified as user activity on Reddit and active searches on Wikipedia pages, is mainly driven by media coverage; meanwhile, this activity declines rapidly while news exposure and COVID-19 incidence remain high. Furthermore, using an unsupervised, dynamic topic modeling approach, we show that while the levels of attention dedicated to different topics by media outlets and internet users are in good accordance, interesting deviations emerge in their temporal patterns.

CONCLUSIONS

Overall, our findings offer an additional key to interpret public perception and response to the current global health emergency and raise questions about the effects of attention saturation on people's collective awareness and risk perception and thus on their tendencies toward behavioral change.

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

Multiple sclerosis coverage in the written media of a low prevalence country

BACKGROUND

Awareness in the community is an important factor across a wide range of diseases and the communication media have an important role in its promotion. However, misinformation and misguide may take place heightening the expectations of people affected by chronic conditions such as multiple sclerosis (MS). This study explores media coverage of MS in a low prevalence country.

METHODS

We identified the most important written media at national and local levels and performed a search in their digital archives and social media with the words "Multiple Sclerosis". The articles found were categorized as relevant, and non-relevant. We describe the total number, number of relevant and non-relevant articles published every year, since the earliest found until 2018. We identified the topics covered by the relevant articles and described their distribution and performed a quality evaluation of their content.

RESULTS

We reviewed the archives of 20 sources. A total of 976 articles where MS was mentioned were reviewed (relevant: 143 [14.6%]; non-relevant: 833 [85.4%]). We observed a steady increase in the annual publication rate, from the first in 1991 up to 107 in 2018. The most frequent covered topic was disease modifying therapies and MS itself, and the least documented topic was rehabilitation. Most of the relevant articles had low quality scores.

CONCLUSION

The media coverage of different topics MS has risen steadily since its first appearance in the early nineties. This should be encouraged, but caution should be held so misinformation is not propagated. We call for the public to discuss misleading information with their healthcare providers.

Optimal strategies for vaccination and social distancing in a game-theoretic epidemiologic model

For various infectious diseases, vaccination has become a major intervention strategy. However, the importance of social distancing has recently been highlighted during the ongoing COVID-19 pandemic. In the absence of vaccination, or when vaccine efficacy is poor, social distancing may help to curb the spread of new virus strains. However, both vaccination and social distancing are associated with various costs. It is critical to consider these costs in addition to the benefits of these strategies when determining the optimal rates of application of control strategies. We developed a game-theoretic epidemiological model that considers vaccination and social distancing under the assumption that individuals pursue the maximization of payoffs. By using this model, we identified the individually optimal strategy based on the Nash strategy when both strategies are available and when only one strategy is available. Furthermore, we determined the relative costs of control strategies at which individuals preferentially adopt vaccination over social distancing (or vice versa).

Trending on Social Media: Integrating Social Media into Infectious Disease Dynamics

Social media plays an important role in alerting and educating the public during disease outbreaks. By increasing awareness of the disease and its prevention, it can lead to a modification of behaviour which then affects contact/incidence rates. Social media data may also be used when formulating, developing and parameterising models. As mobile technology continues to evolve and proliferate, social media is expected to occupy an increasingly prominent role in the field of infectious disease modelling to improve their predictive power. This article presents a review of existing models incorporating media in general and highlights opportunities for social media to enhance traditional compartmental models so as to make the best use of this resource in controlling the spread of disease.

Modeling influenza transmission dynamics with media coverage data of the 2009 H1N1 outbreak in Korea

Recurrent outbreaks of the influenza virus continue to pose a serious health threat all over the world. The role of mass media becomes increasingly important in modeling infectious disease transmission dynamics since it can provide public health information that influences risk perception and health behaviors. Motivated by the recent 2009 H1N1 influenza pandemic outbreak in South Korea, a mathematical model has been developed. In this work, a previous influenza transmission model is modified by incorporating two distinct media effect terms in the transmission rate function; (1) a theory-based media effect term is defined as a function of the number of infected people and its rage of change and (2) a data-based media effect term employs the real-world media coverage data during the same period of the 2009 influenza outbreak. The transmission rate and the media parameters are estimated through the least-squares fitting of the influenza model with two media effect terms to the 2009 H1N1 cumulative number of confirmed cases. The impacts of media effect terms are investigated in terms of incidence and cumulative incidence. Our results highlight that the theory-based and data-based media effect terms have almost the same influence on the influenza dynamics under the parameters obtained in this study. Numerical simulations suggest that the media can have a positive influence on influenza dynamics; more media coverage leads to a reduced peak size and final epidemic size of influenza.

The impact of media on the spatiotemporal pattern dynamics of a reaction-diffusion epidemic model

In this paper, a reaction-diffusion SI epidemic model with media impact is considered. The boundedness of system and the existence of the state are given. The local stabilities of the endemic states are analyzed. Sufficient conditions of the occurrence of the Turing pattern are obtained by the center manifold theorem and normal form method. Some numerical simulations are given to check in the theoretical results. We find that the influence of media not only inhibits the spread of infectious diseases, but also effects the spatial steady-state of model.

New estimates of the Zika virus epidemic attack rate in Northeastern Brazil from 2015 to 2016: A modelling analysis based on Guillain-Barré Syndrome (GBS) surveillance data

BACKGROUND

Between January 2015 and August 2016, two epidemic waves of Zika virus (ZIKV) disease swept the Northeastern (NE) region of Brazil. As a result, two waves of Guillain-Barré Syndrome (GBS) were observed concurrently. The mandatory reporting of ZIKV disease began region-wide in February 2016, and it is believed that ZIKV cases were significantly under-reported before that. The changing reporting rate has made it difficult to estimate the ZIKV infection attack rate, and studies in the literature vary widely from 17% to > 50%. The same applies to other key epidemiological parameters. In contrast, the diagnosis and reporting of GBS cases were reasonably reliable given the severity and easy recognition of the disease symptoms. In this paper, we aim to estimate the real number of ZIKV cases (i.e., the infection attack rate) and their dynamics in time, by scaling up from GBS surveillance data in NE Brazil.

METHODOLOGY

A mathematical compartmental model is constructed that makes it possible to infer the true epidemic dynamics of ZIKV cases based on surveillance data of excess GBS cases. The model includes the possibility that asymptomatic ZIKV cases are infectious. The model is fitted to the GBS surveillance data and the key epidemiological parameters are inferred by using a plug-and-play likelihood-based estimation. We make use of regional weather data to determine possible climate-driven impacts on the reproductive number [Formula: see text], and to infer the true ZIKV epidemic dynamics.

FINDINGS AND CONCLUSIONS

The GBS surveillance data can be used to study ZIKV epidemics and may be appropriate when ZIKV reporting rates are not well understood. The overall infection attack rate (IAR) of ZIKV is estimated to be 24.1% (95% confidence interval: 17.1%-29.3%) of the population. By examining various asymptomatic scenarios, the IAR is likely to be lower than 33% over the two ZIKV waves. The risk rate from symptomatic ZIKV infection to develop GBS was estimated as ρ = 0.0061% (95% CI: 0.0050%-0.0086%) which is significantly less than current estimates. We found a positive association between local temperature and the basic reproduction number, [Formula: see text]. Our analysis revealed that asymptomatic infections affect the estimation of ZIKV epidemics and need to also be carefully considered in related modelling studies. According to the estimated effective reproduction number and population wide susceptibility, we comment that a ZIKV outbreak would be unlikely in NE Brazil in the near future.

A stochastic SIR epidemic model with Lévy jump and media coverage

A stochastic susceptible-infectious-recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global positive solution for the epidemic model is obtained. Sufficient conditions are derived to guarantee that the epidemic disease is extinct and persistent in the mean. The threshold behavior is discussed. Numerical simulations are given to verify our theoretical results.

A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

Local risk perception enhances epidemic control

As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual willingness to take precautions may be influenced by global factors, such as news media, or local factors, such as infected family members or friends. Here, we compare three modes of epidemiological decision-making in the midst of a growing outbreak using network-based mathematical models that capture plausible heterogeneity in human contact patterns. Individuals decide whether to adopt a recommended intervention based on overall disease prevalence, the proportion of social contacts infected, or the number of social contacts infected. While all strategies can substantially mitigate transmission, vaccinating (or self isolating) based on the number of infected acquaintances is expected to prevent the most infections while requiring the fewest intervention resources. Unlike the other strategies, it has a substantial herd effect, providing indirect protection to a large fraction of the population.