scholarly journals Parameterization and Forecasting of Childhood Pneumonia Model Using Least Square Approximation, Lagrange Polynomial and Monte Carlo Simulation

2020 ◽  
pp. 102-114
Author(s):  
Cyrus Gitonga Ngari ◽  
Dominic Makaa Kitavi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Basic Reproduction Number ◽  
Total Population ◽  
Reproduction Number ◽  
Research Result ◽  
Least Square ◽  
Under Five

Despite a study by [1] proposing a simple model of under five years pneumonia, doubt lingers regarding its reliability, sufficiency and validity. The research question is whether the model is valid for use or not?  The objectives of this study were to: incorporate exit rate from under five-year age bracket in the model, use Kenya data to parameterize the model, taking into account the uncertainties and finally to predict the dynamics of pneumonia. The model was rescaled through nondimensionalization. Data was fitted using theory of general solutions of nonlinear Ordinary differential equations, numerical differentiation using Lagrange polynomials and least square approximation method. Uncertainties due to disparities and round off errors were simulated using Monte Carlo simulation. Predictions of dynamics of pneumonia were carried out using MATLAB inbuilt ode solvers. Excel software was used to predict dynamics of discrete ordinary differential equations and to fit data. The basic reproduction number (  and effective reproduction number ( ) were obtained as  Iteration of uncertainties on R was carried out 1000 times by Monte Carlo simulation. The maximum and minimum R were obtained as 90 and 55, respectively. Using MATLAB software and effective reproduction number, the ratio of infective class to the total population and the ratio of class under treatment to the total population will remain constant at 0.095 and 0.2297 respectively for the years 2021, 2022 and 2023. Research result indicted that it is more effective and efficient to use effective reproduction number ( ) than basic reproduction number (  in mathematical modelling of Infectious diseases whenever study focuses on proportion of population. On basis of large absolute errors in fitting data to model, findings cast doubt on model formulation and/or observed data.

scholarly journals An Introduction to The Basic Reproduction Number in Mathematical Epidemiology

2018 ◽  
Vol 62 ◽  
pp. 123-138 ◽  
Author(s):  
Antoine Perasso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Basic Reproduction Number ◽  
Matrix Method ◽  
Reproduction Number ◽  
Mathematical Epidemiology ◽  
Pde Model ◽  
Mathematical Definition ◽  
Next Generation Matrix ◽  
The Basic Reproduction Number

This article introduces the notion of basic reproduction number R0 in mathematical epi-demiology. After an historic reminder describing the steps leading to the statement of its mathematical definition, we explain the next-generation matrix method allowing its calculation in the case of epidemic models described by ordinary differential equations (ODEs). The article then focuses, through four ODEs examples and an infection load structured PDE model, on the usefulness of the R0 to address biological as well mathematical issues.

Analysis of a mathematical model for Dengue-Chikungunya

2017 ◽  
pp. 2933-2940
Author(s):  
Oscar A. Manrique A. ◽  
Dalia M. Munoz P. ◽  
Anibal Munoz L. ◽  
Mauricio Ropero P. ◽  
Steven Raigosa O. ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Epidemic Threshold ◽  
Infectious Process ◽  
Linear Ordinary Differential Equations ◽  
Next Generation Matrix

A dynamical system of non-linear ordinary differential equations which describes the Dengue-Chikungunya infectious process is reported. In this model it is considered the presence of two viruses transmitted by the same vector. Taking into account this fact, we have determined the epidemic threshold, basic reproduction number, using the next generation matrix. The simulations of the differential equations system are carried out with the MATLAB software.

scholarly journals Time delay epidemic model for COVID-19

2020 ◽  
Author(s):  
Montri Maleewong
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Delay ◽  
Disease Control ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Policy Performance ◽  
Delay Effects ◽  
The Basic Reproduction Number

AbstractA time delay epidemic model is presented for the spread of the Coronavirus 2019 (COVID-19) in China. The time delay effects affect infected individuals. Monte Carlo simulation is performed to estimate the transmission and recovery rates. The basic reproduction number is estimated in terms of the average infected ratio. This ratio can be used to monitor the policy performance of disease control during the spread of the disease.

scholarly journals Prediction of the Peak, Effect of Intervention, and Total Infected by COVID-19 in India

2020 ◽  
pp. 1-11
Author(s):  
Parth Vipul Shah
Keyword(s):  
Health Care ◽  
Infection Rate ◽  
Compartmental Model ◽  
Total Population ◽  
Reproduction Number ◽  
Least Square Method ◽  
Peak Effect ◽  
Least Square ◽  
Intervention Period ◽  
Care Capacity

ABSTRACT Objectives: We study the effect of the coronavirus disease 2019 (COVID-19) in India and model the epidemic to guide those involved in formulating policy and building health-care capacity. Methods: This effect is studied using the Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model. We estimate the infection rate using a least square method with Poisson noise and calculate the reproduction number. Results: The infection rate is estimated to be 0.270 and the reproduction number to be 2.70. The approximate peak of the epidemic will be August 9, 2020. A 25% drop in infection rate will delay the peak by 11 d for a 1-mo intervention period. The total infected individuals in India will be 9% of the total population. Conclusions: The predictions are sensitive to changes in the behavior of people and their practice of social distancing.

scholarly journals A TWO-STRAIN EPIDEMIC MODEL WITH UNCERTAINTY IN THE INTERACTION

2012 ◽  
Vol 54 (1-2) ◽  
pp. 108-115 ◽  
Author(s):  
M. G. ROBERTS
Keyword(s):  
Differential Equations ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Influenza A ◽  
Reproduction Number ◽  
The Other ◽  
Orthogonal Functions ◽  
Dependent Variables ◽  
Independent Variable ◽  
Cross Immunity

AbstractAnnual epidemics of influenza A typically involve two subtypes, with a degree of cross-immunity. We present a model of an epidemic of two interacting viruses, where the degree of cross-immunity may be unknown. We treat the unknown as a second independent variable, and expand the dependent variables in orthogonal functions of this variable. The resulting set of differential equations is solved numerically. We show that if the population is initially more susceptible to one variant, if that variant invades earlier, or if it has a higher basic reproduction number than the other variant, then its dynamics are largely unaffected by cross-immunity. In contrast, the dynamics of the other variant may be considerably restricted.

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