期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 32, 期 10, 页码 2037-2076出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202522500488
关键词
Epidemiology; kinetic equations; SIS model; opinion dynamics
资金
- Universidad de Buenos Aires [20020170100456BA]
- CONICET PIP [11220200102806CO]
In this study, we investigate the spread of a disease in a population with different levels of awareness. We introduce a government agent that aims to control the average awareness level to ensure the eradication of the disease. By proposing three levels of analysis, we derive nonlinear systems of equations to describe the evolution of the disease and the response of the government.
We study the propagation of a disease in a population where agents are characterized by their awareness level, representing the measures they take to avoid the infection. We introduce another agent, the government, which is constantly sending a message to the population trying to steer the mean awareness to a value which should ensure the extinction of the disease. We propose three levels to analyze this model. First, an agent-based model, which we use later to derive a mean-field system of ordinary differential equations; and finally, we propose a kinetic approach to model the evolution of the distribution of agents on the awareness levels. We obtain nonlinear systems of different dimension, first an ODE-Boltzmann system and later an ODEs-PDE system, where a Boltzmann or a first order, non-local partial differential equation are coupled with two ordinary differential equations that describe the evolution of the epidemic and the response of the government. We prove the existence and uniqueness of solutions in an abstract setting. Finally, we consider stubborn agents that are not willing to apply protection measures.
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