| 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. |
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