相关论文: Convex Optimization of the Basic Reproduction Numb…

Most epidemic models are spatially aggregate and the index which is most used for planning and policy numbers, the r number, typically refers to a single system of interest. Even if r numbers are calculated for each of adjacent areas,…

The effective reproduction number $R_t$ measures an infectious disease's transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches…

This paper deals with the problem of estimating variables in nonlinear models for the spread of disease and its application to the COVID-19 epidemic. First unconstrained methods are revisited and they are shown to correspond to the…

Accurate estimates of the reproduction ratio are crucial to project infectious disease epidemic evolution and guide public health response. Here, we prove that estimates of the reproduction ratio based on inference from surveillance data…

Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally…

In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…

This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe…

We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In previous work a basic reproduction number $R_0$ is defined with the property that if $R_0<1$ the infection dies out within $O(\log N)$…

Basic and instantaneous reproduction numbers, "R" _"0" and "R" _"t" , are important metrics to assess progress of an epidemic and effectiveness of preventative interventions undertaken, and also to estimate coverage needed for vaccination.…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

In this study we analyze the evolution of the effective reproduction number, $R$, through a SIR spreading process in heterogeneous networks; Characterizing its decay process allows to analytically study the effects of countermeasures on the…

Reproduction numbers, like the basic reproduction number $\mathcal{R}_0$, play an important role in the analysis and application of dynamic models, including contagion models and ecological population models. One difficulty in deriving…

Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the R0 alternative"…

Inference of the reproduction number through time is of vital importance during an epidemic outbreak. Typically, epidemiologists tackle this using observed prevalence or incidence data. However, prevalence and incidence data alone is often…

In epidemiology, the effective reproduction number $R_e$ is used to characterize the growth rate of an epidemic outbreak. In this paper, we investigate properties of $R_e$ for a modified SEIR model of COVID-19 in the city of Houston, TX…

Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection…

Although pandemics are often studied as if populations are well-mixed, disease transmission networks exhibit a multi-scale structure stretching from the individual all the way up to the entire globe. The COVID-19 pandemic has led to an…

We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimension, and its infinite dimensional generalization we introduced in previous works. In this…

Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, conventional reproduction numbers of an overall network do not indicate where an epidemic is spreading.…

In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We…