# Exploring the Effect of Misinformation on Infectious Disease Transmission

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## Abstract

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## 1. Introduction

- Karafillakis and Larson [11] identified the most common reasons for vaccine hesitancy, namely, perceptions that: (1) new vaccines are developed too quickly resulting in insufficient testing; (2) a pandemic is not a life-threatening illness, and is comparable to mild flu; and (3) a vaccine could cause disease and long-term adverse reactions;
- Lorini et al. [7] summarised the ‘3C’ model of factors for vaccine hesitancy. The factors that influence the vaccination decision are: (1) complacency, as people do not value the vaccine as a need, (2) convenience, in that the vaccine is difficult to access, and (3) confidence, as the vaccine or provider is not trusted;
- Wiyeh et al. [12] described the spread of vaccine hesitancy as an “outbreak”. The researchers make a distinction between vaccine hesitancy behaviours: baseline vaccine hesitancy, which refers to the level of refusal or delay in vaccine acceptance that is constantly present in the population and, while it may vary, changes are unlikely to be sudden; reactive vaccine hesitancy, where the delay in acceptance due to vaccine-related events shows a rapid spike in hesitancy levels, usually subsiding at a slow rate.

## 2. Literature Review

#### 2.1. Related Information, Fear and Rumour Spreading Dynamic Models

#### 2.2. Related Infectious Disease and Vaccination Dynamic Models

## 3. Material and Methods

#### 3.1. System Dynamics Sensitivity Analysis Combined with Loop Impact Analysis

- Positive feedback loop (reinforcing), a feedback loop is positive if a change in the source variable will cause the target to change in the same direction;
- Negative feedback loop (balancing), a feedback loop is negative if a change in the source variable will cause the target to change in the opposite direction.

- Dominant loop: A loop that is primarily responsible for model behaviour over some time interval is known as a dominant loop [40];
- Dominant structure: A model’s dominant structure is a subset of the model’s feedback structure, which is responsible for the model’s particular behaviour;
- Point of inflection (POI): A point of inflection is a time of notable change in a model’s behaviour. It is a point on the logistic curve where the loop reaches half of its maximum value.

#### 3.2. LTM Method

- The link score is computed for stocks, connectors, and flows. It measures the contribution and polarity of a link between an independent variable and a dependent variable;
- The loop score is computed as a product of link scores. It measures the contribution of a feedback loop to the behaviour of the model and is indicative of the feedback polarity;
- The relative loop score is a normalised loop score measure taking on a value between −1 and 1. It reports the polarity and fractional contribution of a feedback loop to the change in the value of all stocks at a point in time [47].

#### 3.3. The Misinformation/Disease Model Structure

_{0}d (6) is an input to the disease model and is used to determine the per capita contact rate βd (8). R

_{0}d is the average number of secondary disease-infectious cases that one case generates in a fully susceptible population. In this model, R

_{0}d is set to 3 given that the R

_{0}plausible value for the spread of influenza infectious diseases is between 1.5–4 [49]. The infection rate IRd (10) of disease is the product of the force of infection λd (9) and Susceptible Disease (1). The recovery rate RRd (11) of disease is a function of Infected Disease (2) and the recovery time Duration Infected to Disease (7). A vaccination policy is included in the model to make individuals immune from infectious diseases. The Becoming Vaccinated flow (13) is defined by Susceptible Disease (1), Becoming Vaccinated Fraction (12), and Vaccine Confidence (34). The disease model’s Attack Rate (14) is the proportion of individuals who get infected throughout the full simulation run.

_{0}d = 3

_{0}d/(Duration Infected to Disease × Total Population)

Fraction × Vaccine Confidence(t)

_{0}m (18) is an input to the model and drives the per capita contact value βm (20). R

_{0}m is an average number of secondary misinformation infectious cases that one misinformation infected case would generate in the total misinformation susceptible population. In this research, the R

_{0}m is initially set to 12, which is based on indicative values from rumour models [25,26,28]. The infection rate IRm (22) for misinformation is the product of the force of infection λm (21) and Susceptible Vaccine Misinformation (15). The recovery rate RRm (23) of misinformation is a function of Infected Vaccine Misinformation (16) and Duration Infected to Vaccine Misinformation (19). Normally, when people have high vaccine confidence then there is a beneficial side effect, which improves an individual’s immunity from misinformation. Therefore, the Susceptible Vaccine Misinformation individuals move into the Recovered Vaccine Misinformation via Becoming Immune flow (25). Hence, the Becoming Immune flow is defined by Susceptible Vaccine Misinformation (15), Becoming Immune Fraction (24) and Vaccine Confidence (34).

_{0}m = 12

_{0}m/(Duration Infected to Vaccine Misinformation × Total Population)

#### 3.4. The Misinformation/Disease Model Interaction

#### 3.5. The Misinformation/Disease Model Feedback Loops

_{3}loop consists of 2 stocks and 5 variables. It is a reinforcing loop between the two stocks: Vaccine Confidence and Total Vaccinated. It shows that vaccinated individuals strengthen vaccine confidence and higher vaccine confidence supports the vaccination process. Loop R

_{4}consists of 3 stocks and 7 variables. It is a reinforcing loop between the three stocks: Vaccine Confidence, Susceptible Vaccine Misinformation, and Infected Vaccine Misinformation. It indicates that an increase in vaccine confidence decreases the spread of vaccine misinformation, which in turn, boosts vaccine confidence. The B

_{5}loop consists of 1 stock and 2 variables. It is a balancing loop between Vaccine Confidence and Change in Vaccine Confidence. It shows that a change in vaccine confidence flow adjusts the vaccine confidence level and balances system behaviour. Table 1 lists all the reinforcing and balancing feedback loop numbers, the process description, the loop’s stocks, and the variables’ details.

## 4. Experimental Results

_{0}d, R

_{0}m, and the remaining variables have fixed values. R

_{0}m and R

_{0}d can vary, and plausible ranges are selected [28,49].

#### 4.1. Exploring a Range of R_{0} Values

_{0}m = 6, R

_{0}d = 2) to the highest (R

_{0}m = 18, R

_{0}d = 4). The results show the significant impact of increased misinformation contagion on the disease attack rate. For example, consider the results shown in Table 4 taking one row at a time. They show that by keeping the R

_{0}d constant, there is a corresponding increase in the attack rate due to the extra contagion effect from misinformation. For example, for an R

_{0}d = 3 in S4, the attack rate increases by 75.6% in S6 (from 0.23 to 0.404), thereby showing the sensitivity of the attack rate to increases in R

_{0}m. Scenario S9 shows the highest disease Attack Rate, where both R

_{0}d and R

_{0}m values are at their highest.

#### 4.2. Sensitivity Analysis for Scenarios SA1 to SA6

- The highest median value for the disease attack rate is scenario SA6, where R
_{0}d is fixed at four, and R_{0}m varies between six and eighteen. This shows the potential impact that a strong misinformation contagion process has on the outcome; - Scenario SA1 has the R
_{0}m at six, although, even with this low value, the maximum disease attack rate is high at over 40%. This shows reduced vaccine confidence results in lower vaccine uptake; - Scenario SA3 shows a significant increase in the disease attack rate as compared to SA1 and SA2, where R
_{0}d varies between two and four, and R_{0}m is fixed at 18. This shows the impact of high misinformation, which leads to lower vaccine uptake, thereby providing the disease with more opportunities to spread. - There is an overall pattern whereby varying R
_{0}m (SA4, SA5, and SA6) has a higher impact on the disease attack rate than varying R_{0}d (SA1, SA2, and SA3).

#### 4.3. The Scenarios S1 to S9 with LTM Analysis

_{0}m and R

_{0}d on the model’s feedback loops. Figure 5 presents a visual comparison between model runs from two of the scenarios, S2 (R

_{0}d = 2, R

_{0}m = 12) and S5 (R

_{0}d = 3, R

_{0}m = 12). The area plot displays the contribution of each loop to model behaviour over time, where the total across all loops will add up to 100%. The plots show the feedback loops’ behaviours on the y-axis from 0% to 100% (where 50% is the point where the loop score becomes dominant), and the model run time on the x-axis. The four reinforcing loops (red colour) and seven balancing loops (blue colour) are shown over the entire period of the model’s simulation, T

_{0}to T

_{100}. In both scenarios, S2 and S5, the initial run time from T

_{0}to T

_{30}shows that reinforcing feedback loops cover almost 55% of the area and there are a few points of inflection (POI). In both scenarios, S2 (R

_{0}d = 2, R

_{0}m = 12) and S5 (R

_{0}d = 3, R

_{0}m = 12), the final run time, T

_{30}to T

_{100}, shows a prominent increase in the balancing feedback loop’s coverage. The scenario S2 (R

_{0}d = 2, R

_{0}m = 12) and S5 (R

_{0}d = 3, R

_{0}m = 12) comparisons show minor changes in the reinforcing and balancing feedback loops’ behaviours.

_{0}m varies between 12 and 18, and R

_{0}d is fixed at two. The scenarios show a prominent change in the feedback loops’ behaviours. In both scenarios, S2 (R

_{0}d = 2, R

_{0}m = 12) and S3 (R

_{0}d = 2, R

_{0}m = 18), the initial run time from T

_{0}to T

_{30}shows that reinforcing feedback loops cover almost 55% of the area. In scenario S3 (R

_{0}d = 2, R

_{0}m = 18), the final run time from T

_{30}to T

_{100}shows multiple points of inflection (POI), where the balancing feedback loop area increases but the reinforcing behaviour is continues to have an influence, as they still cover almost 40% of the area (e.g., loop R

_{1}), which is due to the impact of high misinformation. Therefore, a higher misinformation scenario can be seen to increase reinforcing behaviour and decrease balancing behaviour.

_{0}m and R

_{0}d on the model’s reinforcing and balancing feedback loops’ behaviours and the following results are of interest:

- When R
_{0}d is fixed at two, and R_{0}m varies between 12 and 18, scenarios S1, S2, and S3 show a notable change in the reinforcing loops’ average relative scores, from 17% to 41%. However, with R_{0}m fixed at six, when R_{0}d varies, (S1, S4, and S7) the reinforcing loops’ average relative scores do not increase. This suggests that the variation in R_{0}m has a bigger impact on the reinforcing loops’ dominance; - When R
_{0}d equals three and R_{0}m varies between six and eighteen (S4, S5, and S6), the reinforcing loops’ average relative scores change from 18% to 29%. With R_{0}m fixed at 12 (S2, S5, and S8), the reinforcing contribution increases from 24% to 42%; - When R
_{0}d equals four, and R_{0}m varies between 12 and 18 (S7, S8, and S9), the reinforcing loops’ average relative scores change from 16% to 23%. With R_{0}m fixed at 18 (S3, S6, and S9), the reinforcing contribution decreases from 41% to 23%. The decline in the reinforcing contribution is caused by vaccine confidence stock, which is a goal-seeking structure. The result shows that high disease and misinformation impact model feedback loops scores and the vaccine confidence stock’s goal-seeking structure adjust the vaccine confidence level.

_{0}m and R

_{0}d impact the dominant share of the reinforcing and balancing feedback loops.

R_{0}m | Low Value (L) = 6 | Feedback Loop’s Score | Medium Value (M) = 12 | Feedback Loop’s Score | High Value (H) = 18 | Feedback Loop’s Score | |
---|---|---|---|---|---|---|---|

R_{0}d | |||||||

Low Value (L) = 2 | S1 | R = 17.69% B = 82.31% | S2 | R = 24.19% B = 75.81% | S3 | R = 41.21% B = 58.79% | |

Medium Value (M) = 3 | S4 | R = 18.1% B = 81.9% | S5 | R = 24.06% B = 75.94% | S6 | R = 29.57% B = 70.43% | |

High Value (H) = 4 | S7 | R = 16.26% B = 83.74% | S8 | R = 42.03% B = 57.97% | S9 | R = 23.16% B = 76.84% |

#### 4.4. Sensitivity Analysis SA1 to SA6 Combined with LTM

_{0}m and R

_{0}d on the model’s feedback loops’ behaviours using sensitivity analysis combined with LTM. The analysis is based on the sensitivity analysis for scenarios SA1 through to SA6. The experiment varies R

_{0}m and R

_{0}d to explore the impact on the negative feedback loop B

_{5}(vaccine confidence adjustment). Figure 8 presents the scenarios (SA1 to SA6) to show impact on the negative feedback loop B

_{5}(vaccine confidence adjustment).

- Scenario SA6 shows the highest impact for the B
_{5}(vaccine confidence adjustment) feedback loop, where R_{0}d is fixed at four, and R_{0}m varies between six and eighteen. The B_{5}(vaccine confidence adjustment) feedback loop’s relative score increases by more than −25%. This shows the potential impact of the misinformation contagion process; - Scenario SA1 shows the least impact for the B
_{5}(vaccine confidence adjustment) feedback loop, where R_{0}m is fixed at six, and R_{0}d varies between two and four, although even with this low value, the B_{5}(vaccine confidence adjustment) feedback loop’s relative score increases by almost −22%. This shows the impact of reduced vaccine confidence, leading to a change in the vaccine confidence rate; - Scenario SA3 also shows an impact on the B
_{5}(vaccine confidence adjustment) feedback loop, where R_{0}d varies between two and four, and R_{0}m is fixed at 18. The B_{5}(vaccine confidence adjustment) feedback loop’s relative score is almost −25%. This shows the effect of high misinformation, leading to lower vaccine uptake; - Scenario SA4 shows an increase for the B
_{5}(vaccine confidence adjustment) feedback loop score, where R_{0}d is fixed at two, and R_{0}m varies between six and eighteen, although, even with this low value of R_{0}d, the B_{5}(vaccine confidence adjustment) feedback loop’s relative score increases by almost −19%. This shows the impact of R_{0}m and R_{0}d, leading to change in the vaccine confidence and disease attack rate; - The analysis shows a pattern whereby varying R
_{0}m (SA4, SA5, and SA6) has a higher impact on the loop score for B_{5}(vaccine confidence adjustment) and disease attack rate, as well than varying R_{0}d (SA1, SA2, and SA3).

## 5. Conclusions

_{0}m escalated the disease Attack Rate, whereas higher R

_{0}m more significantly increased the disease Attack Rate. The model feedback loops analysis also indicated that R

_{0}m affected the reinforcing and balancing feedback loops’ relative scores and increased the disease Attack Rate. Sensitivity analysis combined with LTM establishes confidence in the usefulness of this model, as it shows how misinformation can significantly impact the disease attack rate.

_{0}m and the results of vaccine confidence surveys; (2) extending the model to different age cohorts to explore heterogeneities between a range of groups in terms of vaccine confidence and disease spread; and (3) extending the loop dominance analysis to include techniques such as the eigenvalue elasticity analysis, (EEA) and the partway participation method (PPM).

## Supplementary Materials

_{1}and B

_{1}Loops’ Relative Scores in Line Plot. Figure S3. R

_{1}and B

_{1}Loops’ Relative Scores in Stacked Area Plot. Figure S4. The R

_{1}and B

_{1}Relative Loops’ Scores against S and I Stocks. Table S1. The R

_{1}and B

_{1}Loops’ Details. Table S2. Demonstration Link Scores for S→IR, λ→IR and I→λ by using Equation (S1). Calculations are based on the equations: IR = S*λ and λ = I*β. Table S3. Demonstration Link Scores for IR→S and IR→I by using Equation (S2). Table S4. Demonstration Loop Scores and Relative Loop Scores for the B

_{1}and R

_{1}.

## Author Contributions

## Funding

## Conflicts of Interest

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**Table 1.**The misinformation/disease model’s 11 feedback loops. Positive links are shown in red and negative links are shown in blue.

Loop ID | Loop Description | Loop Variables |
---|---|---|

R_{1} | Misinformation contagion process | Infected Vaccine Misinformation → λm → IRm → Infected Vaccine Misinformation |

R_{2} | Disease contagion process | Infected Disease → λd → IRd → Infected Disease |

R_{3} | Vaccine Confidence leads to more vaccinations, which in turn increase Vaccine Confidence | Vaccine Confidence → Becoming Vaccinated → Total Vaccinated → Confidence Indicator → Change in Vaccine Confidence → Vaccine Confidence |

R_{4} | Vaccine Confidence reduces the spread of misinformation, which increases Vaccine Confidence | Vaccine Confidence → Becoming Immune → Susceptible Vaccine Misinformation → IRm → Infected Vaccine Misinformation → Confidence Indicator → Change in Vaccine Confidence → Vaccine Confidence |

B_{1} | Misinformation recovery | Infected Vaccine Misinformation → RRm → Infected Vaccine Misinformation |

B_{2} | Disease recovery | Infected Disease → RRd → Infected Disease |

B_{3} | Immune to misinformation reduces misinformation vulnerability | Susceptible Vaccine Misinformation → Becoming Immune → Susceptible Vaccine Misinformation |

B_{4} | Vaccination reduces disease vulnerability | Susceptible Disease → Becoming Vaccinated → Susceptible Disease |

B_{5} | Vaccine confidence adjustment | Vaccine Confidence → Change in Vaccine Confidence → Vaccine Confidence |

B_{6} | Depletion disease | Susceptible Disease → IRd → Susceptible Disease |

B_{7} | Depletion misinformation | Susceptible Vaccine Misinformation → IRm → Susceptible Vaccine Misinformation |

R_{0}m | Low Value (L) = 6 | Medium Value (M) = 12 | High Value (H) = 18 | |
---|---|---|---|---|

R_{0}d | ||||

Low Value (L) = 2 | S1 | S2 | S3 | |

Medium Value (M) = 3 | S4 | S5 | S6 | |

High Value (H) = 4 | S7 | S8 | S9 |

No | R_{0}m | R_{0}d |
---|---|---|

SA1 | R_{0}m = 6 (Low) | R_{0}d = Uniform (2,4) |

SA2 | R_{0}m = 12 (Medium) | R_{0}d = Uniform (2,4) |

SA3 | R_{0}m = 18 (High) | R_{0}d = Uniform (2,4) |

SA4 | R_{0}m = Uniform (6,18) | R_{0}d = 2 (Low) |

SA5 | R_{0}m = Uniform (6,18) | R_{0}d = 3 (Medium) |

SA6 | R_{0}m = Uniform (6,18) | R_{0}d = 4 (High) |

R_{0}m | Low Value (L) = 6 | Disease Attack Rate | Medium Value (M) = 12 | Disease Attack Rate | High Value (H) = 18 | Disease Attack Rate | |
---|---|---|---|---|---|---|---|

R_{0}d | |||||||

Low Value (L) = 2 | S1 | 0.01 | S2 | 0.012 | S3 | 0.057 | |

Medium Value (M) = 3 | S4 | 0.23 | S5 | 0.243 | S6 | 0.404 | |

High Value (H) = 4 | S7 | 0.545 | S8 | 0.557 | S9 | 0.602 |

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**MDPI and ACS Style**

Mumtaz, N.; Green, C.; Duggan, J.
Exploring the Effect of Misinformation on Infectious Disease Transmission. *Systems* **2022**, *10*, 50.
https://doi.org/10.3390/systems10020050

**AMA Style**

Mumtaz N, Green C, Duggan J.
Exploring the Effect of Misinformation on Infectious Disease Transmission. *Systems*. 2022; 10(2):50.
https://doi.org/10.3390/systems10020050

**Chicago/Turabian Style**

Mumtaz, Nabeela, Caroline Green, and Jim Duggan.
2022. "Exploring the Effect of Misinformation on Infectious Disease Transmission" *Systems* 10, no. 2: 50.
https://doi.org/10.3390/systems10020050