979 research outputs found
SEIR epidemiological model with varying infectivity and infinite delay
A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R-0, which is a threshold quantity for the stability of equilibria, is calculated. If R-0 1, then an endemic equilibrium appears which is locally asymptotically stable. Applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when R-0 > 1
Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model
We study variants of the SEIR model for interpreting some qualitative
features of the statistics of the Covid-19 epidemic in France. Standard SEIR
models distinguish essentially two regimes: either the disease is controlled
and the number of infected people rapidly decreases, or the disease spreads and
contaminates a significant fraction of the population until herd immunity is
achieved. After lockdown, at first sight it seems that social distancing is not
enough to control the outbreak. We discuss here a possible explanation, namely
that the lockdown is creating social heterogeneity: even if a large majority of
the population complies with the lockdown rules, a small fraction of the
population still has to maintain a normal or high level of social interactions,
such as health workers, providers of essential services, etc. This results in
an apparent high level of epidemic propagation as measured through
re-estimations of the basic reproduction ratio. However, these measures are
limited to averages, while variance inside the population plays an essential
role on the peak and the size of the epidemic outbreak and tends to lower these
two indicators. We provide theoretical and numerical results to sustain such a
view
Nonlinear incidence and stability of infectious disease models
In this paper we consider the impact of the form of the non-linearity of the infectious disease incidence rate on the dynamics of epidemiological models. We consider a very general form of the non-linear incidence rate (in fact, we assumed that the incidence rate is given by an arbitrary function f (S, I, N) constrained by a few biologically feasible conditions) and a variety of epidemiological models. We show that under the constant population size assumption, these models exhibit asymptotically stable steady states. Precisely, we demonstrate that the concavity of the incidence rate with respect to the number of infective individuals is a sufficient condition for stability. If the incidence rate is concave in the number of the infectives, the models we consider have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case the infection-free equilibrium state is stable. For the incidence rate of the form g(I)h(S), we prove global stability, constructing a Lyapunov function and using the direct Lyapunov method. It is remarkable that the system dynamics is independent of how the incidence rate depends on the number of susceptible individuals. We demonstrate this result using a SIRS model and a SEIRS model as case studies. For other compartment epidemic models, the analysis is quite similar, and the same conclusion, namely stability of the equilibrium states, holds
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