The Basic Reproduction Number of Infectious Diseases: Computation and Estimation Using Compartmental Epidemic Models

2009 ◽  
pp. 1-30 ◽  
Author(s):  
Gerardo Chowell ◽  
Fred Brauer
Keyword(s):  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Epidemic Models ◽  
The Basic Reproduction Number

scholarly journals Rich Dynamics of a Brucellosis Model with Transport

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Juan Liang ◽  
Zhirong Zhao ◽  
Can Li
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Great Influence ◽  
Stable State ◽  
Initial Values ◽  
Si Model ◽  
The Basic Reproduction Number

Brucellosis is one of the major infectious diseases in China. In this study, we consider an SI model of animal brucellosis with transport. The basic reproduction number ℛ0 is obtained, and the stable state of the equilibria is analyzed. Numerical simulation shows that different initial values have a great influence on results of the model. In addition, the sensitivity analysis of ℛ0 with respect to different parameters is analyzed. The results reveal that the transport has dual effects. Specifically, transport can lead to increase in the number of infected animals; besides, transport can also reduce the number of infected animals in a certain range. The analysis shows that the number of infected animals can be controlled if animals are transported reasonably.

scholarly journals Epidemic management with admissible and robust invariant sets

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257598
Author(s):  
Willem Esterhuizen ◽  
Jean Lévine ◽  
Stefan Streif
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Intervention Strategies ◽  
Epidemic Models ◽  
Invariant Sets ◽  
Social Distancing ◽  
The Basic Reproduction Number

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.

scholarly journals Analysis and Prediction of COVID-19 Characteristics Using a Birth-and-Death Model

2020 ◽  
Author(s):  
Narayanan C. Viswanath
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Explicit Expression ◽  
Basic Reproduction Number ◽  
Stationary Point ◽  
Reproduction Number ◽  
Sir Model ◽  
Expected Number ◽  
Infection Period ◽  
The Basic Reproduction Number

AbstractIts spreading speed together with the risk of fatality might be the main characteristic that separates COVID-19 from other infectious diseases in our recent history. In this scenario, mathematical modeling for predicting the spread of the disease could have great value in containing the disease. Several very recent papers have contributed to this purpose. In this study we propose a birth-and-death model for predicting the number of COVID-19 active cases. It relation to the Susceptible-Infected-Recovered (SIR) model has been discussed. An explicit expression for the expected number of active cases helps us to identify a stationary point on the infection curve, where the infection ceases increasing. Parameters of the model are estimated by fitting the expressions for active and total reported cases simultaneously. We analyzed the movement of the stationary point and the basic reproduction number during the infection period up to the 20th of April 2020. These provide information about the disease progression path and therefore could be really useful in designing containment strategies.

scholarly journals Studies on the basic reproduction number in stochastic epidemic models with random perturbations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andrés Ríos-Gutiérrez ◽  
Soledad Torres ◽  
Viswanathan Arunachalam
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Survival Function ◽  
Epidemic Models ◽  
Random Perturbations ◽  
Asymptotically Stable ◽  
Stochastic Epidemic Models ◽  
Stochastic Epidemic ◽  
Disease Free ◽  
The Basic Reproduction Number

AbstractIn this paper, we discuss the basic reproduction number of stochastic epidemic models with random perturbations. We define the basic reproduction number in epidemic models by using the integral of a function or survival function. We study the systems of stochastic differential equations for SIR, SIS, and SEIR models and their stability analysis. Some results on deterministic epidemic models are also obtained. We give the numerical conditions for which the disease-free equilibrium point is asymptotically stable.

Sign in / Sign up

Export Citation Format

Share Document