On incidence-dependent management strategies against a SEIRS epidemic:
extinction of the epidemic using Allee effect
Abstract
We develop a mathematical model to study the effects of
non-pharmaceutical interventions (NPIs) on the dynamics of an epidemic.
The level of intervention is assessed as a fraction of the population
being isolated and depends on the level of incidence of the epidemic in
the population. We perform the mathematical analysis of the model and
show that, depending on the choice of the prevalence-dependent isolation
function, it is possible to create new endemic equilibria and to change
the stability of the disease-free equilibrium for which the epidemic
vanishes. The model is then applied to the case of the covid-19
pandemic. Several NPI management strategies are considered. In the case
of a NPI intensity increasing with the level of infection, it is
possible to avoid the initial epidemic peak of great amplitude that
would have occurred without intervention and to stabilize the epidemic
at a chosen and sufficiently low endemic level. In the case of a NPI
intensity decreasing with the level of infection, the epidemic can be
driven to extinction by generating an “Allee” effect: when the
incidence is below a given level, the epidemic goes extinct while above
it, the epidemic will still be able take hold at a lower endemic level.
Simulations illustrate that appropriate NPIs could make the Covid-19
vanish relatively fast. We show that in the context of the covid-19
pandemic, most countries have not chosen to use the most efficient
strategies.