Important Concepts in Mathematical Modeling of Infectious Diseases

2018 ◽  
pp. 1-33 ◽  
Author(s):  
Michael Y. Li
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases

SIR-based mathematical modeling of infectious diseases with vaccination and waning immunity

2019 ◽  
Vol 37 ◽  
pp. 101027 ◽  
Author(s):  
Matthias Ehrhardt ◽  
Ján Gašper ◽  
Soňa Kilianová
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Waning Immunity

scholarly journals IV. Mathematical Modeling and Control of Infectious Diseases

2020 ◽  
Vol 109 (11) ◽  
pp. 2276-2280
Author(s):  
Ayako Suzuki ◽  
Hiroshi Nishiura
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Modeling And Control ◽  
And Control

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 Mathematical Modeling and Simulation of SIR Model for COVID−2019 Epidemic Outbreak: A Case Study of India

2020 ◽  
Author(s):  
Dr. Ramjeet Singh Yadav
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
Initial Level ◽  
Sir Model ◽  
Euler Method ◽  
Epidemic Outbreak

The present study discusses the spread of COVID−2019 epidemic of India and its end by using SIR model. Here we have discussed about the spread of COVID−2019 epidemic in great detail using Euler method. The Euler method is a method for solving the ordinary differential equations. The SIR model has the combination of three ordinary differential equations. In this study, we have used the data of COVID−2019 Outbreak of India on 8 May, 2020. In this data, we have used 135710 susceptible cases, 54340 infectious cases and 1830 reward/removed cases for the initial level of experimental purpose. Data about a wide variety of infectious diseases has been analyzed with the help of SIR model. Therefore, this model has been already well tested for infectious diseases by various scientists and researchers. Using the data to the number of COVID−2019 outbreak cases in India the results obtained from the analysis and simulation of this proposed SIR model showing that the COVID−2019 epidemic cases increase for some time and there after this outbreak decrease. The results obtained from the SIR model also suggest that the Euler method can be used to predict transmission and prevent the COVID−2019 epidemic in India. Finally, from this study, we have found that the outbreak of COVID−2019 epidemic in India will be at its peak on 25 May 2020 and after that it will work slowly and on the verge of ending in the first or second week of August 2020.

scholarly journals Effect of daily human movement on some characteristics of dengue dynamics

2020 ◽  
Author(s):  
Mayra R. Tocto-Erazo ◽  
Daniel Olmos-Liceaga ◽  
José A. Montoya-Laos
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Numerical Simulations ◽  
High Activity ◽  
Human Movement ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Key Factor ◽  
Low Activity ◽  
Outbreak Size

Human movement is a key factor in infectious diseases spread such as dengue. Here, we explore a mathematical modeling approach based on a system of ordinary differential equations to study the effect of human movement on characteristics of dengue dynamics such as the existence of endemic equilibria, and the start, duration, and amplitude of the outbreak. The model considers that every day is divided into two periods: high-activity and low-activity. Periodic human movement between patches occurs in discrete times. Based on numerical simulations, we show unexpected scenarios such as the disease extinction in regions where the local basic reproductive number is greater than 1. In the same way, we obtain scenarios where outbreaks appear despite the fact that the local basic reproductive numbers in these regions are less than 1 and the outbreak size depends on the length of high-activity and low-activity periods.

How to stop a vampiric infection? Using mathematical modeling to fight infectious diseases

2013 ◽  
Vol 7 ◽  
pp. 4195-4202
Author(s):  
Wadim Strielkowski ◽  
Evgeny Lisin ◽  
Emily Welkins
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases

Mathematical modeling of infectious diseases

Science ◽  
2015 ◽  
Vol 347 (6227) ◽  
pp. 1213-1213 ◽  
Author(s):  
C. Ash
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases
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