Over the last two decades, large-scale outbreaks of infectious diseases have resulted in high levels of morbidity, mortality, and overall economic burden for affected regions. As complex networks become increasingly popular tools of study, researchers are applying network theory to the field of epidemiology.

Due to the plethora of disease-related data available from various media outlets, an individual's behavioral response to and communication of an epidemic depends on the pattern of information flow in a separate yet related network. As a result, mathematical models of humans' reactions to disease outbreaks are important tools in epidemiological analysis.

In an article publishing next week in the SIAM Journal on Applied Mathematics, researchers employ a concrete interplay model in quenched multiplex networks to study the connection between adaptive human behavior and epidemic spread. They base their model — which illustrates these factors as separate layers in the networks — on a standard susceptible-infected-susceptible model. Its generality makes it applicable to a wide range of public health scenarios.

Members of an affected population typically base their behavioral responses on information gleaned from mass and social media, physical encounters in their social and spatial neighborhoods, and general observations. "Traditionally, infectious disease models have treated human behaviors as constant, implying that they do not fluctuate according to disease incidence or a characteristic timescale," Sun and Fu said.

Humans adopt preventative measures based on these direct or indirect relations, both to protect themselves from infection and reduce the risk of further disease transmission. Such measures include limitation or elimination of time spent outside the home, increased attention to hand-washing and personal hygiene, and limited contact with neighbors and other citizens.

Prior studies involving complex interplay models have classified awareness into three categories: local awareness, global awareness, and contact awareness. However, Sun et al. classify it into two alternative categories: (i) adaptive behaviors stemming from awareness and (ii) behavioral information transmission.

Sun and Fu said. "We also find that behavioral control for some individuals enhances the speed with which the epidemic tends to become stable and the speed of collective synchronization, and also significantly reduces the value of the highest peak of the infection's prevalence. This suggests that our epidemic control strategy from the perspective of behavioral control is very valid."

Outbreak of severe acute respiratory syndrome

To test their model, the authors apply it to an outbreak of severe acute respiratory syndrome (SARS), a contagious and dangerous respiratory illness. Because no vaccines currently exist for SARS, public health measures are primarily responsible for its control. Sun et al. focus on two types of minor preventative measures from the most recent outbreak: transmission precautions and contact precautions.

"The analysis suggests that a rapid behavioral response, a combination of public health measures, and the regulation of public institutions for certain key individuals (those with more connections) can effectively curb the outbreak of SARS by decreasing cumulative infections and deaths and reducing the reproductive number," Sun and Lee said. 

"The numerical results show that individual adaptive behaviors triggered by the emergence of an epidemic can slow down the spread of the infection, lower the final epidemic size, and in some cases can prevent the infection from becoming widespread," Small said.

"These results provide us with an alternative idea on understanding why some infections do not cause major outbreaks or reach the epidemic threshold in the absence of immunization policy or territory-wide quarantine and isolation measures."

Sun et al. hope to incorporate realistic data about human behaviors to formulate more practical and applicable models. They plan to specifically investigate the effects of drastic control measures and the impact of the time delay between when individuals become aware of an outbreak and when they modify their behaviors.