Special Session 24: Mathematical and Computational Modeling of Complex Biological Systems

Awareness and compliance in an infectious disease model
Jacques B\\'{e}lair
Universit\\\\\\\\\\\\\\\\'{e} de Montr\\\\\\\\\\\\\\\\'{e}al
Canada
Co-Author(s):    
Abstract:
Management of the COVID-19 pandemic required in its early stages the deployment of non pharmaceutical interventions (NPIs) [social isolation, physical distancing, mask-wearing, hand-washing]. We consider a compartmental model of disease propagation in which information is the infection: knowledge of, and compliance with, measures limiting the propagation of an infectious disease (such as non-pharmaceutical interventions (NPIs)) are modeled as dynamic parameters. The population is divided in three classes: unaware individuals, aware but noncompliant and aware and compliant individuals so that the model takes the form, in its simplest form, of the equations \[ \left\{ \begin{array}{ll} S_0'(t) &= \mu -\beta A S_0 -\mu S_0\ S_1(t) &=  (1-p)\beta S_0 A - \beta S_1 A-\mu S_1 +\gamma(A) A\ A'(t) &= \beta (pS_0+S_1)A-(\mu +\gamma(A))A \end{array} \right. \] Conditions for the existence of multiple stable equilibria will be discussed as well as the consequences for the control of the infection.