A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy

Abstract

We introduce a compartmental epidemic model to describe the spread of COVID-19 within a population, assuming that a vaccine is available, but vaccination is not mandatory. The model takes into account vaccine hesitancy and the refusal of vaccination by individuals, which take their decision on vaccination based on both the present and past information about the spread of the disease. Theoretical analysis and simulations show that voluntary vaccination can certainly reduce the impact of the disease but is unable to eliminate it. We also demonstrate how the information-related parameters affect the dynamics of the disease. In particular, vaccine hesitancy and refusal are better contained in case of widespread information coverage and short-term memory. Finally, the possible impact of seasonality on the spread of the disease is investigated.

Keywords: Human behaviour; Infectious disease; Seasonality; Stability; Vaccination.

Fig. 1

Flow chart for the COVID-19 model (3)–(5). The population $N\left(t\right)$ is divided into six disjoint compartments of individuals: susceptible $S\left(t\right)$, exposed $E\left(t\right)$, asymptomatic $I_a\left(t\right)$, symptomatic $I_s\left(t\right)$, vaccinated $V\left(t\right)$ and recovered $R\left(t\right)$. Blue colour indicates the information-dependent process in the model, with $M\left(t\right)$ ruled by (3f).

Fig. 2

Dynamics in the absence of vaccination (${\phi }_0=0$ days⁻¹, D = 0). Total infectious cases (panel A) and cumulative disease-induced deaths (panel B) as predicted by model (3)–(14) (black lines) compared with Italian official data (Italian Ministry of Health, 2020b) (blue dots), in the period 16 August–13 October 2020. Initial conditions and other parameter values are given in Table 1.

Fig. 3

Panel A: Contour plot of the control reproduction number ${\mathcal{R}}_V$(9) versus the information-independent constant vaccination rate, ${\phi }_0$, and the factor of vaccine ineffectiveness, $\sigma$. Intersection of dotted black lines indicates the value corresponding to the baseline scenario: ${\phi }_0=0.002$ days⁻¹, σ = 0.2. Panel B: Plot of ${\mathcal{R}}_V$ versus $\sigma$, by setting ${\phi }_0=0.002$ days⁻¹ (black line) and ${\phi }_0=2·{10}^{-5}$ days⁻¹ (blue line). Other parameters’ values are given in Table 1.

Fig. 4

VAX-0 case. Temporal dynamics of susceptible individuals S (panel A), vaccinated individuals V (panel B), symptomatic infectious individuals $I_s$ (panel C), and cumulative deaths CD (panel D), as predicted by model (3)–(14). Blue lines: constant vaccination with ${\phi }_0=0.002$ days⁻¹, D = 0; black lines: information–dependent vaccination with ${\phi }_0=0.002$ days⁻¹, D = 500μ/Λ; red lines: constant vaccination with ${\phi }_0={\phi }_0^{p1},D=0$; green lines: constant vaccination with ${\phi }_0={\phi }_0^{p2},D=0$. Initial conditions and other parameter values are given in Table 1 and Section 5.1.

Fig. 5

Information-dependent vaccination case (${\phi }_0=0.002$ days⁻¹, D = 500μ/Λ). Temporal dynamics of the ratio between the information-dependent component, ${\phi }_1\left(M\right)$, and the constant component, ${\phi }_0$, of the vaccination rate. Black line: VAX-0 case; blue line: VAX-30 case. Initial conditions and other parameter values are given in Table 1.

Fig. 6

Impact of the information coverage, k, and the average delay, $T_a=a^{-1}$, on the VAX-0 scenario as depicted by contour plots. Panel A: cumulative vaccinated individuals at the final time $t_f=365$ days, CV$\left(t_f\right)$. Panel B: time of symptomatic prevalence peak, arg$\max \left(I_s\right)$. Panel C: cumulative deaths at the final time $t_f=365$ days, CD$\left(t_f\right)$. The intersection of dotted white lines indicates the values corresponding to the baseline scenario: $k=0.8$ and $T_a=3$ days. Initial conditions and other parameter values are given in Table 1.

Fig. 7

Impact of the factor of vaccine ineffectiveness, $\sigma$, and the information-independent constant vaccination rate, ${\phi }_0$, on the scenario VAX-0 with constant vaccination (i.e., $D=0$) as illustrated by contour plots. Panel A: cumulative vaccinated individuals at the final time $t_f=365$ days, CV$\left(t_f\right)$. Panel B: time at symptomatic prevalence peak, arg$\max \left(I_s\right)$. Panel C: cumulative deaths at the final time $t_f=365$ days, CD$\left(t_f\right)$. The intersection of dotted white lines indicates the values corresponding to the baseline scenario: $\sigma =0.2$ and ${\phi }_0=0.002$ days⁻¹. Initial conditions and other parameter values are given in Table 1.

Fig. 8

Impact of the factor of vaccine ineffectiveness, $\sigma$, and the information-independent constant vaccination rate, ${\phi }_0$, on the scenario VAX-0 with information–dependent vaccination (i.e., $D=500\mu /\mathrm{\Lambda }$), as shown by contour plots. Panel A: cumulative vaccinated individuals at the final time $t_f=365$ days, CV$\left(t_f\right)$. Panel B: time when symptomatic prevalence peak is reached, arg$\max \left(I_s\right)$. Panel C: cumulative deaths at the final time $t_f=365$ days, CD$\left(t_f\right)$. The intersection of dotted white lines indicates the values corresponding to the baseline scenario: $\sigma =0.2$ and ${\phi }_0=0.002$ days⁻¹. Initial conditions and other parameter values are given in Table 1.

Fig. 9

Impact of the information coverage, k, and the transmission rate, $\beta$, on the VAX-0 scenario as shown by contour plots. Panel A: cumulative vaccinated individuals at the final time $t_f=365$ days, CV$\left(t_f\right)$. Panel B: time of symptomatic prevalence peak, arg$\max \left(I_s\right)$. Panel C: cumulative deaths at the final time $t_f=365$ days, CD$\left(t_f\right)$. The intersection of dotted white lines indicates the values corresponding to the baseline scenario: $k=0.8$ and $\beta =2.699·{10}^{-8}$ days⁻¹. Initial conditions and other parameter values are given in Table 1.

Fig. 10

Impact of the information delay, $T_a=a^{-1}$, and the transmission rate, $\beta$, on the VAX-0 scenario as shown by contour plots. Panel A: cumulative vaccinated individuals at the final time $t_f=365$ days, CV$\left(t_f\right)$. Panel B: time of symptomatic prevalence peak, arg$\max \left(I_s\right)$. Panel C: cumulative deaths at the final time $t_f=365$ days, CD$\left(t_f\right)$. The intersection of dotted white lines indicates the values corresponding to the baseline scenario: $T_a=3$ days and $\beta =2.699·{10}^{-8}$ days⁻¹. Initial conditions and other parameter values are given in Table 1.

Fig. 11

Impact of the seasonality on the information–dependent vaccination case (${\phi }_0=0.002$ days⁻¹, D = 500μ/Λ). Temporal dynamics of symptomatic infectious individuals $I_s$ (panel A), and cumulative deaths CD$\left(t\right)$ (panel B), as predicted by model (3)–(14). Blue lines: VAX-0S case (i.e., scenario including seasonality); black lines: VAX-0 case (i.e., no–seasonality scenario). Initial conditions and other parameter values are given in Table 1 and Section 6.