1,635 research outputs found
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
A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence
Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form for the case p<1 are constructed. Global stability of the models is thereby established
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
Predicting unobserved exposures from seasonal epidemic data
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR)
epidemiological model with a contact rate that fluctuates seasonally. Through
the use of a nonlinear, stochastic projection, we are able to analytically
determine the lower dimensional manifold on which the deterministic and
stochastic dynamics correctly interact. Our method produces a low dimensional
stochastic model that captures the same timing of disease outbreak and the same
amplitude and phase of recurrent behavior seen in the high dimensional model.
Given seasonal epidemic data consisting of the number of infectious
individuals, our method enables a data-based model prediction of the number of
unobserved exposed individuals over very long times.Comment: 24 pages, 6 figures; Final version in Bulletin of Mathematical
Biolog
- …