A behaviour and disease transmission model: incorporating the Health Belief Model for human behaviour into a simple transmission model

Abstract

The health and economic impacts of infectious diseases such as COVID-19 affect all levels of a community from the individual to the governing bodies. However, the spread of an infectious disease is intricately linked to the behaviour of the people within a community since crowd behaviour affects individual human behaviour, while human behaviour affects infection spread, and infection spread affects human behaviour. Capturing these feedback loops of behaviour and infection is a well-known challenge in infectious disease modelling. Here, we investigate the interface of behavioural science theory and infectious disease modelling to explore behaviour and disease (BaD) transmission models. Specifically, we incorporate a visible protective behaviour into the susceptible-infectious-recovered-susceptible (SIRS) transmission model using the socio-psychological Health Belief Model to motivate behavioural uptake and abandonment. We characterize the mathematical thresholds for BaD emergence in the BaD SIRS model and the feasible steady states. We also explore, under different infectious disease scenarios, the effects of a fully protective behaviour on long-term disease prevalence in a community, and describe how BaD modelling can investigate non-pharmaceutical interventions that target-specific components of the Health Belief Model. This transdisciplinary BaD modelling approach may reduce the health and economic impacts of future epidemics.

Keywords: Health Belief Model; behaviour modelling; epidemiology; transmission modelling.

Figure 1.

A BaD SIRS model without demography. The parameters are defined in table 1.

Figure 2.

The Health Belief Model [24,25], adapted from Brailsford et al. [32]. The blue boxes are the incentives for performing a given health behaviour, and the orange boxes are the barriers that prevent an individual from performing the behaviour. The boxes with both colours can both positively and negatively affect whether someone performs the health behaviour.

Figure 3.

Possible equilibrium states from the BaD SIRS transmission model, where dark blue is the BaD-free equilibrium ( ${\displaystyle E_{00}}$ ), light blue is the behaviour-free-disease endemic equilibrium ( ${\displaystyle E_{0D}}$ ), light red is the behaviour endemic-disease free equilibrium ( ${\displaystyle E_{B0}}$ ) and dark red is the BaD endemic equilibrium ( ${\displaystyle E_{BD}}$ ). (a) No fear of disease or spontaneous uptake of behaviour ( ${\displaystyle {\omega }_2={\omega }_3}$ = 0). (b) Fear of disease but no spontaneous uptake of behaviour ( ${\displaystyle {\omega }_2=8,{\omega }_3=0}$ ). (c) Both fear of disease and spontaneous uptake of behaviour ( ${\displaystyle {\omega }_2=8,{\omega }_3=0.2}$ ). Along the ${\displaystyle x}$ -axis, we vary ${\displaystyle \beta }$ through the disease characteristic ${\displaystyle {\mathcal{R}}_0^D}$ , and along the ${\displaystyle y}$ -axis, we vary ${\displaystyle {\omega }_1}$ through the behavioural characteristic ${\displaystyle {\mathcal{R}}_0^B}$ . We have set ${\displaystyle p=c=0.5}$ , and all other parameters take values as in table 1. The vertical black line represents ${\displaystyle {\mathcal{R}}_0^D=1}$ whereas the horizontal/curved black line shows ${\displaystyle {\mathcal{R}}_0=1}$ . For a given behavioural characteristic ${\displaystyle {\mathcal{R}}_0^B}$ , points on the horizontal/curved black line represent the critical values ${\displaystyle {\mathcal{R}}_0^{D\ast }}$ of the disease characteristic where a disease endemic state becomes feasible.

Figure 4.

The difference in endemic disease prevalence between a population performing no health behaviours, compared to a population performing a fully protective health behaviour with ${\displaystyle p=c=1}$ for a COVID-19-like ( ${\displaystyle {\mathcal{R}}_0^D=8.4}$ , (a ,b)) and an influenza-like ( ${\displaystyle {\mathcal{R}}_0^D=1.5}$ , (c ,d)) illness. All other parameters take the values in table 1. (a) Difference in long-term disease prevalence between the two populations for a COVID-19-like illness ( ${\displaystyle {\mathcal{R}}_0^D=8.2}$ ); the dotted vertical line is the proportion of the population performing the behaviour ( ${\displaystyle B^{\ast }=0.22}$ ) for the parameters given in table 1 and ${\displaystyle \beta =8.2}$ . (b) Phase plane of susceptible versus infectious individuals for a COVID-19-like illness ( ${\displaystyle {\mathcal{R}}_0^D=8.2}$ ), where the orange dotted line shows the trajectory for a population with no health behaviour and the blue solid line shows the trajectory for a population with a fully protective health behaviour; the proportion of the population performing the behaviour in the long term is ${\displaystyle B^{\ast }=0.22}$ . (c) Difference in long-term disease prevalence between the two populations for an influenza-like illness ( ${\displaystyle {\mathcal{R}}_0^D=1.5}$ ); the dotted vertical line is the proportion of the population performing the behaviour ( ${\displaystyle B^{\ast }=0.15}$ ) for the parameters given in table 1 and ${\displaystyle \beta =1.5}$ . (d) Phase plane of susceptible versus infectious individuals for an influenza-like illness ( ${\displaystyle {\mathcal{R}}_0^D=1.5}$ ), where the orange dotted line shows the trajectory for a population with no health behaviour and the blue solid line shows the trajectory for a population with a fully protective health behaviour; the proportion of the population performing the behaviour in the long term is ${\displaystyle B^{\ast }=0.15}$ .

Figure 5.

The effect of intervention strategies targeted at components of the Health Belief Model on endemic disease prevalence. The ${\displaystyle x}$ -axis is the disease characteristic ${\displaystyle {\mathcal{R}}_0^D}$ , and the ${\displaystyle y}$ -axis is the endemic disease prevalence. The vertical dotted lines represent an influenza-like disease characteristic ( ${\displaystyle {\mathcal{R}}_0^D=1.5}$ ) and a COVID-19-like disease characteristic ( ${\displaystyle {\mathcal{R}}_0^D=8.2}$ ). The lines show a no-behaviour SIRS model (black), a base-line BaD SIRS model (light blue), a good intervention doubling (or halving) the effect (red), and an excellent intervention quadrupling (or quartering) the effect (yellow). (a) Social cues to action ( ${\displaystyle {\omega }_1}$ ). (b) Perception of illness threat ( ${\displaystyle {\omega }_2}$ ). (c) Self-efficacy and perceived benefits of behaviour ( ${\displaystyle {\omega }_3}$ ). (d) Social cues for abandonment ( ${\displaystyle {\alpha }_1}$ ). (e) Internal cues to action and perceived barriers to behaviour ( ${\displaystyle {\alpha }_2}$ ). Baseline parameter values are defined in table 1 with ${\displaystyle p=c=0.5}$ .