Estimating epidemic exponential growth rate and basic reproduction number

The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic,and is also closely related to the basic reproduction number.Estimating the growth rate from the epidemic curve can be a challenge,because of its decays with time.For fast epidemics,the estimation is subject to over-fitting due to the limited number of data points available,which also limits our choice of models for the epidemic curve.We discuss the estimation of the growth rate using maximum likelihood method and simple models.

Estimating the quarantine failure rate for COVID-19

Quarantine is a crucial control measure in reducing imported COVID-19 cases and community transmissions.However,some quarantined COVID-19 patients may show symptoms after finishing quarantine due to a long median incubation period,potentially causing community transmissions.To assess the recommended 14-day quarantine policy,we develop a formula to estimate the quarantine failure rate from the incubation period distribution and the epidemic curve.We found that the quarantine failure rate increases with the exponential growth rate of the epidemic curve.We apply our formula to United States,Canada,and Hubei Province,China.Before the lockdown of Wuhan City,the quarantine failure rate in Hubei Province is about 4.1%.If the epidemic curve flattens or slowly decreases,the failure rate is less than 2.8%.The failure rate in US may be as high as 8.3%-11.5%due to a shorter 10-day quarantine period,while the failure rate in Canada may be between 2.5%and 3.9%.A 21-day quarantine period may reduce the failure rate to 0.3%-0.5%.

Age-dependent branching processes in random environments

We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ 0, ξ 1,…) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξ n ) on ?+, and reproduce independently new particles according to a probability law p(ξ n ) on ?. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean E ξ Z(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.

Deviation Property of Periodic Measures in C^1 Non-uniformly Hyperbolic Systems with Limit Domination

In a C1 non-uniformly hyperbolic systems with limit domination, we consider the periodic measures that supported on the Pesin set and keep a distance at least 6 to a hyperbolic ergodic measure μ given before. And then, we bound from top the exponential growth rate of such periodic measures by the supremum of measure theoretic entropy on a closed set.