Modeling learning and forgetting processes with the corresponding impacts on human behaviors in infectious disease epidemics

Highlights

• Two mathematics models for forgetting and learning behavior in epidemic are proposed.

• Protection behavior changes are discussed by the information and emotion.

• Application ranges of two models are determined by analysis and simulations.

• Two models are used to restore 2009 Chicago H1N1 prevalence in agent-based model.

Abstract

This article presents two new mathematical models, an information forgetting curve (IFC) model and a memory reception fading and cumulating (MRFC) model, to examine forgetting and learning behaviors of individuals during an infectious disease epidemic. Both models consider how epidemic prevalence and community behavior-change information may affect agent emotions and subsequently influence an individual's behavior changes during an epidemic. The IFC model utilizes a forgetting curve to process epidemic information, and the MRFC model formulates disease information variations using the Itô diffusion process. Sensitivity analysis and simulation comparisons showed that the MRFC model more accurately describes the epidemic with high lethal rate gets high attention. The author also demonstrated that MRFC model has higher sensitivity parameters and is more flexible on wide ranges of infection rates than the IFC model. However, the IFC model is a better suited for widespread, low-risk mortality epidemics, such as seasonal influenza, the infection information and protective behavior have close relationships among the susceptible population. An agent-based simulation model also developed to mimic the epidemic prevalence of the 2009 Chicago H1N1 using public available historical data sets by IFC model.

Introduction

Human disease awareness and related behavior changes during disease epidemics have recently attracted considerable research attention (Polgar, 1962). In order to be more accurately predict a disease epidemic and estimate its potential impacts, however, a comprehensive understanding of information dissemination within human contact networks and the effects of this information on human emotions, awareness, and behavior must increase. Extensive literature and studies have investigated how information affects human behaviors, but minimal research has focused on human memory and forgetting/learning processes related to disease information, or the process in which information may be forgotten and relearned during an epidemic episode. This paper proposes two new mathematical models to investigate the effects of information in disease transmission, including the forgetting and learning phenomenon.

The human brain cannot store an infinite amount of retrieved information. In 1968, Shiffrin and Atkinson (1969) first classified memory as long term and short term. Engle, Tuholski, Laughlin, and Conway (1999) defined short-term memory as retainable for a short period of time (usually from 6 to 600 s) but unable to be manipulated; however, they did not detail how long-term or short-term memory relates to people forgetting information. Ebbinghaus (1913) experimentally investigated how the process of forgetting proceeds with influences of time or daily events, hypothesizing that, although a memory series is gradually forgotten, memories that have been learned twice fade more slowly compared to memories that have been learned once. Wingfield and Byrnes (2013) proposed a “forgetting curve” to show the process of memory loss over a period from 20 min to 31 days. A recent paper has indicated that the people learn language also following the forgetting curve (Weltens & Cohen, 1989), and experiments have been conducted to increase understanding of the learning and forgetting phenomenon (Badiru, 1992, Bailey, 1989). In 1985, Brainerd, Kingma, and Howe (1985) concluded that forgetting is governed by various laws and therefore requires unique theoretical assumptions.

Notable learning and forgetting mathematical models have been proposed. In 1976, Carlson and Rowe (1976) introduced the variable regression variable forgetting (VRVF) model, and, in 1990, Elm'Aghraby (1990) proposed the variable regression invariant forgetting (VRIF) model, which corrected errors in previous forgetting models and accommodated a finite horizon. In 1996, Jaber and Bonney (1996) proposed the learn-forget curve model (LFCM), which showed that forgetting is dependent on some factors such as the learning slope, the quantity produced and the minimum production breaks. In 1997, Jaber and Bonney (1997) compared these three models, and in recent years, Jaber, Kher, and Davis (2003) reviewed factors that influence forgetting and incorporated the job similarity factor into the LFCM. In 2002, Sikström and Jaber (2002) provided an elaborate review of forgetting curves in psychology and industrial engineering literature. Because the previous papers did not consider the forgetting phenomenon in disease, however, this paper proposes an information forgetting curve model (IFC) to describe how disease information fades over time during an epidemic, following a forgetting curve through time and thereby influencing final disease memory. In 2012, Sikström & Jaber updated their research in the modeling of learning and forgetting area (Sikström & Jaber, 2012). They proposed a Depletion-Power-Integration-Latency (DPIL) Model. This model considered the depletion of the encoding resource as forgetting and learning behavior when the system repetitively performs a task. More than fitting the historical dataset and calculate the settings of optimal performance, this model discussed how learning can interact with the forgetting by modeling the repetitively encoding can increase the memory strength.

Stochastic factors can influence the information perception process and new information can diversely affect human memory when agents receive new information and forget previous information. Researchers (Slovic, 2016) have shown that biased media coverage, misleading personal experiences, and anxieties can cause people to process information with unwarranted confidence or uncertain judgment. Zhao, Wu, Kuang, Bi, and Ben-Arieh (2018) also discussed the stochastic change rate of perception to infectious disease risk. This paper proposes a memory reception fading and cumulating (MRFC) model to describe the stochastic phenomenon of human memory as it pertains to disease information based on learning and forgetting.

Agents have unique understandings based on identical information, and they react with distinct switch behaviors. In 2009, Chen (2009) concluded that agents learn prevalence through the spread of information and can adjust human behavior during a disease epidemic. Funk, Gilad, Watkins, and Jansen (2009) found that the spread of disease awareness significantly decreases the infection rate, and Kiss, Cassell, Recker, and Simon (2010) proved that the diffusion of disease information increases risk awareness and causes the host population to take infection prevention measures. In 2015, Zhao, Wu, Kuang, and Ben-Arieh (2015) proposed a disease model using a spatial evolutionary game to illustrate the impact of information dissemination on human behavior in an epidemic, proving that how an agent feels depends on information content and context (Nahl & Bilal, 2007). In other words, agents demonstrate unique perspectives for the same disease information, resulting in diverse emotional responses. When disease information is positive, agents may have minimal concerns about the disease; negative information, however, may increase agent's awareness. Hence, certain types of information could alter agents’ moods or emotions (Pessoa, 2008). Chen, Bi, Zhao, Ben-Arieh, and Wu (2017) also modeled how disease information, such as the number of infected individuals and the number of susceptible individuals who choose the switching behaviors, impact agents' fears about the epidemic. This paper applies an agent-based model to determine how disease information can cause diverse human behaviors, as well as use of the one-factor-at-a-time method (OFAT) to conduct sensitivity analysis for various parameter settings in the IFC and MRFC models, highlighting the influence of parameter settings for the model and comparing agents’ epidemic behaviors using the IFC, MRFC, and no-memory models.

This paper also discusses the 2009 H1N1 influenza epidemic. By combining historical infection data in affected cities with corresponding population characteristics, the authors restored the 2009 H1N1 prevalence in Chicago, a typical H1N1-affected city. This paper also investigates how the phenomenon of memory fading and behavior-switched protection influence epidemic spreading.