Impact of opinion formation phenomena in epidemic dynamics: kinetic modeling on networks

TL;DR

This work extends a conventional compartmental framework including behavioral attitudes in shaping public opinion and promoting the adoption of protective measures under the influence of different degrees of connectivity to offer a more nuanced understanding of epidemic dynamics in the context of modern information dissemination and social behavior.

Abstract

After the recent COVID-19 outbreaks, it became increasingly evident that individuals' thoughts and beliefs can have a strong impact on disease transmission. It becomes therefore important to understand how information and opinions on protective measures evolve during epidemics. To this end, incorporating the impact of social media is essential to take into account the hierarchical structure of these platforms. In this context, we present a novel approach to take into account the interplay between infectious disease dynamics and socially-structured opinion dynamics. Our work extends a conventional compartmental framework including behavioral attitudes in shaping public opinion and promoting the adoption of protective measures under the influence of different degrees of connectivity. The proposed approach is capable to reproduce the emergence of epidemic waves. Specifically, it provides a clear link between the social influence of highly connected individuals and the epidemic dynamics. Through a heterogeneity of numerical tests we show how this comprehensive framework offers a more nuanced understanding of epidemic dynamics in the context of modern information dissemination and social behavior.

Figures (8)

• Figure 4.1: Test 1. Evolution in time of the marginal distribution of the opinions (upper row) and the normalized marginal distribution of opinions both for the entire population and for $c>10 \overline c$ at $t=100$ (bottom row), for the case $\tau_1=1$ and $\tau_2=10^{-2}$ (left), $\tau_1=1$ and $\tau_2=1$ (center), and $\tau_1=10^{-2}$ and $\tau_2=1$ (right).
• Figure 4.2: Test 2. Evolution in time of the mass (upper row) and of the first moment with respect to the opinions (bottom row) of each compartment solving the macroscopic system \ref{['eq:seiropicont_rho']}-\ref{['eq:seiropicont_mw']} with $\tau_1 = 1$ and $\tau_2 = 10$, compared to the ones reconstructed from the solution of the kinetic system \ref{['eq:seiropicont']} with scaling \ref{['eq:scaling_lambda']} for the same values on $\tau_1, \tau_2$ and $\lambda = 1,10^{-3}$.
• Figure 4.3: Test 3. ( $\tau_1 = \tau_2 = 1$). Time evolution of the marginal density of opinions (left) and comparison between the normalized terminal marginal of opinions both for the entire population and for $c>10 \overline c$ (right), for Setting 1 (upper row) and Setting 2 (bottom row).
• Figure 4.4: Test 3. ($\tau_1 = 10^{-2}$ and $\tau_2 = 10^{-3}$). Time evolution of the marginal density of opinions (left) and comparison between the normalized terminal marginal of opinions both for the entire population and for $c>10 \overline c$ (right). Upper row refers to Setting 1, bottom row refers to Setting 2.
• Figure 4.5: Test 3. Time evolution of the infected population $\rho_I(t)$ considering Setting 1, and Setting 2, respectively when influencers are against and in favor of protective measures.The black solid line indicates the alert level. On the left, the case with $\tau_1=\tau_2=1$ and on the right, $\tau_1 = 10^{-2}$ and $\tau_2 = 10^{-3}$.

Theorems & Definitions (1)

• proof