Understanding and modeling individuals’ behaviors during epidemics is crucial for effective epidemic control. However, existing research ignores the impact of users’ irrationality on decisionmaking in the epidemic. Meanwhile, existing disease control methods often assume users’ full compliance with measures like mandatory isolation, which does not align with the actual situation. To address these issues, this paper proposes a prospect theorybased framework to model users’ decisionmaking process in epidemics and analyzes how irrationality affects individuals’ behaviors and epidemic dynamics. According to the analysis results, irrationality tends to prompt conservative behaviors when the infection risk is low but encourages riskseeking behaviors when the risk is high. Then, this paper proposes a behavior inducement algorithm to guide individuals’ behaviors and control the spread of disease. Simulations and real user tests validate our analysis, and simulation results show that the proposed behavior inducement algorithm can effectively guide individuals’ behavior.
The outbreak of COVID19 has led to a severe public health crisis and great economic losses. Governments worldwide have taken various measures, including lockdowns and mandatory quarantines, to inhibit the spread of the disease. However, individuals may not comply with these policies, as many have their own opinions and preferences. In such public health crises, individuals tend to act irrationally, such as excessive panic in an epidemic outbreak and underestimation of the dangers of the epidemics in its later spread, which can significantly affect individuals’ decisions and ultimately affect the spread of the epidemic. Moreover, individuals’ behaviors and the epidemic affect each other. For example, individuals’ behaviors such as social distancing, wearing masks, and isolating can inhibit the spread of the epidemic, and individuals tend to choose protective behaviors when the pandemic is more severe. Therefore, it is crucial to model individuals’ behaviors during the epidemic and determine how to control the spread of the epidemic by guiding individuals’ behaviors without resorting to mandatory measures.
In the following, this paper reviews recent works on epidemic control over networks, individual behavior modeling during an epidemic, and irrational behavior modeling.
There are numerous studies on how to control the epidemic spread over networks, and many attempted to inhibit the epidemic spread on a network by removing nodes. Wang et al. pointed out that the epidemic spread on a network is highly correlated with the largest eigenvalue of the graph’s adjacency matrix [
The studies on epidemic control investigated how to control the spread by isolating individuals, restricting population movement, etc. However, these studies all assumed that individuals would comply with the control policies, which is usually not the actual situation. In reality, individuals have their own ideas and may not necessarily obey policies such as isolation and movement restrictions.
Some prior works attempted to model individual behaviors during an epidemic. The studies [
These studies modeled and analyzed individuals’ behavioral choices in the epidemic. However, they did not consider the common and critical issue of individual irrationality, which can significantly affect their decisionmaking process during an epidemic.
Individuals usually resort to irrational decisionmaking when confronted with risks, such as the potential for infection during an epidemic. For instance, many people may be overly panicky in the early stages of an epidemic and may underestimate the risk of the epidemic in the later stages. A challenge here is how to mathematically model such irrational behaviors. Prospect theory provides theoretical models to quantify how individuals tend to overestimate small probabilities and underestimate high probabilities [
The existing studies modeled individuals’ irrationality and simple decisions such as whether to take a vaccination. However, they did not consider the continuous interaction and mutual influence between the epidemic spread and individual choices over time in the context of irrational behaviors.
Our work differs from prior works in two aspects. First, prior works on individual behavior modeling in epidemics either ignore the impact of irrational decisionmaking or fail to consider the continuous interaction and mutual influence between the epidemic spread and individual behaviors. In this paper, the prospect theory is applied to model individuals’ irrational decisions during an epidemic and the coevolution of individuals’ behaviors and the epidemic. We theoretically analyze the impact of the individuals’ irrationality on their decisions as well as the epidemic. Second, existing works on epidemic control assume individuals’ absolute compliance with the government’s policies such as mandatory isolation. In this paper, based on the individual behavioral model, we propose an effective method to guide individuals’ behaviors and control the epidemic spread. In contrast to prior approaches, our disease spread control method does not rely on mandatory measures.
The main contributions of our work are:
We build an Mchoice epidemicbehavior coevolution model to simulate individuals’ irrational decisionmaking and analyze their impact on the epidemic. We theoretically analyze the coevolution of user behavior and epidemic and its steady state. Also, the impact of irrationality on individuals’ behaviors and disease spread is theoretically analyzed.
Given the above individual behavior model, we propose a behavior inducement algorithm to guide individuals’ decisions to control the epidemic.
We validate our individual behavior model and behavior inducement algorithm through simulations. In addition, we use real user tests to validate the conclusions about the impact of irrationality on individuals’ behavior.
The rest of the paper is organized as follows.
Notations  Meaning 

The fractions of susceptible and infected individuals at 

The possible behaviors individuals can adopt  
The proportion of susceptible individuals adopting action 

The actual payoff when behavior 

The loss of being infected  
The infection rate when the individual takes action 

The recovery rate  
The number of individuals  
The degree of the physical contact network and the information network  
The value function of the expected utility theory and prospect theory  
The weighting function of the prospect theory  
The irrationality coefficient  
The steady state of the 2behavior model following the expected utility theory  
The steady state of the 2behavior model following the prospect theory 
During an epidemic, individual behavioral choices and the spread of the disease mutually influence each other. When the probability of infection and the potential losses are high, people tend to adopt protective behaviors, which in turn can inhibit the epidemic spread. In this section, we propose a model to capture the coevolution of individual behavioral choices and disease spread during a pandemic. We consider irrational behavior in our model and use the model with rational behavior assumption as a baseline to analyze the impact of irrationality on the evolutionary dynamics of the epidemic and its steady states. Based on the model presented in [
Following the work in [
Our model consists of two interconnected parts: the disease spread model and the behavior change model. The disease spread model quantifies how the epidemic spreads through the network given the current behaviors of all individuals, and the behavior change model describes how individuals update their behaviors based on the current number of infected individuals and the behaviors of their neighbors. The illustration of our model is in
We use the classic SusceptibleInfectedSusceptible (SIS) model to depict disease spread, which describes the disease spread process using differential equations. In addition to depicting disease spread, this method of differential equations has a wide range of applications, such as describing the spread of viruses in the body [
The individual behavior model quantifies the dynamics of
In
Game theory models strategic interactions among agents, providing insights into decisionmaking across diverse scenarios, from social networks [
In each time slot, every susceptible individual receives a payoff determined by the chosen strategy and interactions with neighbors. In this paper, we consider two scenarios where the susceptible individual is rational and irrational. Therefore, we define the payoff of different behaviors based on the expected utility theory (EUT) [
In our behavior modeling and epidemic control problem, every susceptible individual adopting protective behavior
We consider those epidemics with
Similar to EUT, the value function
In addition, instead of using the actual probability
Given the probability weighting function in
In our problem, same as the analysis of
Note that if the value functions of EUT and PT are identical (i.e.,
In our work, we assume that individuals with different behaviors are uniformly distributed in the entire network. Therefore, the probability that the focal individual
Combining
In reality, even if individuals do not change their behaviors, the proportion of susceptible individuals with different behaviors will change over time due to transitions in health states. Let
Note that
Given
Combining
Based on the disease spread
Here, the first differential equation represents the dynamics of individuals’ health states, and the subsequent
At the steady state, both the proportion of infected individuals
To find the steady state of our Mchoice disease spread and behavior change model, we follow an approach that is similar to [
where
To obtain insights into the coevolution process of epidemic spread and behavioral choice and their steady states, in this section, we consider a simple scenario where each susceptible individual can take two possible behaviors and the theoretical solution of
In this section, based on our model in the previous section, we analyze the evolution of the epidemic and the dynamics of individuals’ choices between two behaviors: the risky behavior (going out) represented by
When all individuals are rational, the payoff is modeled by EUT in
When
From Theorem 1, there are three possible steady states, which correspond to three different situations in reality:
Case 1: The steady state
Case 2: For the steady state
Note that from
Case 3: The steady state
Next, we consider the scenario where all individuals are “irrational”, and model their payoff function using the PT. By substituting the PT utility function
Similarly, we can get the steady state of
When
The three stable states in PT are similar to those in EUT:
Case 1: The steady state (0,1) is the same as Case 1 under EUT. In this situation, the epidemic will always die out, and all individuals will choose the risky behavior.
Case 2: The steady state
Case 3: The steady state
In this section, we analyze the influence of individuals’ irrationality on the steady state. In the weighting function in
When
When
If
When
When
On the contrary, if
When
When
When
In addition, if
On the contrary, if
To better understand Theorem 3, note that in
For Theorem 3b, when
For Theorem 3c, when
Note that from
In summary, irrationality tends to make individuals become more extreme, that is, riskaverse when the risk is small and riskseeking when the risk is high.
In this section, based on our previous analysis in
We first discuss measures that governments can take to guide individuals’ behaviors during an epidemic. For example, they can incentivize or penalize certain behaviors, such as subsidizing risky behaviors (e.g., going out) to boost the economy, penalizing risky behaviors, or encouraging conservative behaviors (such as staying at home and wearing masks) to control the disease spread. In our model, this means the parameters
Next, we discuss the goals of behavior guidance. The first goal is to control the spread of the disease at the steady state. For example, the government may wish to keep the number of infected people as low as possible. Here, the loss caused by the epidemic is represented as
Since the irrationality coefficient should fall within
In this work, we do not specify the specific forms of
From
Given the system parameters and
From our analysis in Appendix F in Supplementary Material, we have the following Theorem 4.
if
If
If
From Theorem 4, we only need to model and solve the problem for Case 3 in
In this section, we consider the following scenario and use it as an example to demonstrate how to model and solve the optimization problem in
Since the infection rate
From Theorem 4, we only need to get the optimal solution in Case 3 and then we can get the optimal solution of the whole space by comparing it with
Note that in
If
According to Theorem 4, the optimization problem can be transformed into the problem in Case 3 and then we can get the optimal solution of the whole space by comparing it with
If
Here,
If the constraints
We can use the same method in
In this section, we first run simulations to validate our steady state analysis of the coevolution process and the effect of irrationality on individuals’ behaviors and epidemic spread in
Theorem 1 and Theorem 2 give theoretical analyses of the steady states when individuals are rational and irrational, respectively. To validate the two theorems, as an example, we conducted simulations on regular networks with 500 nodes. The physical contact network has a fixed degree of 10, while the information network has a degree of 20. We observe similar trends on other types of networks and with other parameters. We set the recovery rate to
Then we validate Theorem 3 and investigate the impact of irrationality on the steady states using the same simulation setup as before.
Before Point A, i.e., when
Between Points A and B,
Between Points B and C,
After Point C,
The above shows an example where irrationality promotes conservative behaviors, and in most parameter settings, irrationality makes individuals more conservative. Appendix I in Supplementary Material shows an example where irrationality makes individuals riskseeking. This situation only occurs when the infection rate is high, and the loss of disease is extremely low.
In summary, the simulation results effectively validate our analysis in Theorem 3.
Then we simulate the behavior inducement algorithm proposed in
The results of the proposed algorithm under feasible constraints are shown in
Simulation results of the proposed behavior inducement algorithm with infeasible constraints are shown in
In summary, from
While the simulation experiments have validated our theoretical analysis, it is necessary to further validate our conclusions using real user tests. However, obtaining real user data on behavioral choices, network structure, and spread data simultaneously poses a significant challenge. Therefore, we qualitatively validate our conclusions through sociological experiments. In our test, 550 subjects were interviewed, including 237 males and 313 females. The distribution of data is provided in Appendix J in Supplementary Material.
In our test, we first collect data to estimate the irrationality coefficient
After the subjects have made their initial choices, a refined set of choices is presented to them to obtain finegrained results. For instance, if a subject chooses option
Similar to [
In
We classify subjects into different groups based on their irrationality coefficient
Moreover, we also plot scatter plots of
Cultural and social elements can influence individual behavioral choices and disease spread, and our model can be used to analyze them to a certain extent.
First, in reality, an individual’s understanding and views of an epidemic may be affected by culture, beliefs, and social environment. For example, people in different countries have different opinions about COVID19 [
In addition, different costs of implementing policies in different cultures and countries can be reflected in our behavior inducement algorithm. For example, in some countries or cultures, the cost of implementing policies is lower, and individuals are more inclined to obey behavioral inducement. In our model, that means they have a lower
In
Through theoretical analysis and experiments, we get some insights into disease spread control, which can guide government policies to a certain extent.
First, considering the practicalities of governance, the government can employ a multifaceted approach to control spread, utilizing methods like incentivizing and penalizing behaviors and raising awareness about the disease through propaganda. Through our experiments, we observe that the efficacy of a singular measure diminishes as its intensity increases. Therefore, employing multiple measures simultaneously can yield superior outcomes at a reduced cost.
Second, the influence of irrationality has great significance. The degree of individual irrationality can be affected by propaganda and other means. Through experiments, we find that changing the irrational coefficient
Finally, as discussed in
In this paper, we propose an epidemicbehavior coevolution framework to analyze the coevolution of user behavior and the disease spread during an epidemic. Our model considers the irrationality of individuals’ decisionmaking processes, and our theoretical analysis shows that individual irrationality polarizes individual behavior choices. That is, irrationality makes users riskaverse when the probability of being infected is small, while they tend to be riskseeking when the probability of being infected is large. We then propose a behavior inducement algorithm to control the disease spread and reduce losses by guiding individual behavior. Simulation results show the correctness of our theoretical analysis and verify the validity of our guidance control method. We also qualitatively prove the correctness of our conclusions using realuser tests. Different from the prior works, in this work, we use prospect theory to model the individuals’ irrational behaviors during an epidemic and the coevolution of individuals’ behaviors and the epidemic. Our research contributes to comprehending the irrational behavioral choices made by individuals during epidemics. Additionally, our behavior inducement approach does not rely on mandatory policies like prior works, providing a viable framework for governments to effectively control disease spread during epidemics.
None.
The authors received no specific funding for this study.
Wenxiang Dong built the model, derived the theory, conducted simulations and real user tests, and wrote the paper. H. Vicky Zhao provided research guidance and edited the paper.
In our ethics application for the real user tests, we promised to protect the privacy of all test subjects. Therefore, we cannot provide the specific data of each sample in the real user tests. The distribution of the data can be provided upon request.
The authors declare that they have no conflicts of interest to report regarding the present study.
The supplementary material is available online at