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 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.

scholarly journals Stability of a Mathematical Model of Malaria Transmission with Relapse

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Guang-Ming Qiu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Next Generation Matrix ◽  
The Government ◽  
Disease Free ◽  
The Basic Reproduction Number

A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction numberR0is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable ifR0≤1, and the system is uniformly persistence ifR0>1. Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.

scholarly journals Government control in increasing vehicles taxpayer compliance

2021 ◽  
Vol 26 ◽  
pp. 502-513
Author(s):  
Diah Anggeraini Hasri ◽  
Zulkieflimansyah Zulkieflimansyah ◽  
Muhammad Nurjihadi ◽  
Nova Adhitya Ananda ◽  
Lukmanul Hakim
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Differential Equations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sensitivity Index ◽  
Control Parameters ◽  
Government Control ◽  
Analysis Tools ◽  
The Basic Reproduction Number

This study aims to determine the dynamics of taxpayer compliance from time to time by using a mathematical model. This study uses two analysis tools, namely differential equations, to create a model of taxpayer compliance and Moderated Regression Analysis to determine the effect of moderating government control on increasing taxpayer compliance. This study indicates that government control can reduce the number of non-compliant taxpayers by looking at the sensitivity index. The results of the sensitivity index of government control parameters can reduce the basic reproduction number. Statistically, it is also proven that the moderation of government control can strengthen the effect of awareness on taxpayer compliance by 82.5%.

scholarly journals Mathematical Assessment of the Dynamical Model of Smoking Tobacco Epidemic in Bangladesh

2020 ◽  
pp. 36-48
Author(s):  
Sk. Abdus Samad ◽  
Md. Tusberul Islam ◽  
Sayed Toufiq Hossain Tomal ◽  
MHA Biswas
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Basic Reproduction Number ◽  
Conversion Rate ◽  
Reproduction Number ◽  
The World ◽  
Tobacco Epidemic ◽  
The Basic Reproduction Number

Bangladesh is one of the largest tobacco users in the world being troubled by smoking related issues. In this paper we consider a compartmental mathematical model of smoking in which the population is divided into five compartments: susceptible, expose, smokers, temporary quitters and permanent quitters described by ordinary differential equations. We study by including the conversion rate from light smoker to permanent quit smokers. The basic reproduction number R0 has been derived and then we found two euilibria of the model one of them is smoking-free and other of them is smoking-present. We establish the positivity, boundedness of the solutions and perform stability analysis of the model. To decrease the smoking propensity in Bangladesh we perform numerical simulation for various estimations of parameters which offer understanding to give up smoking and how they influence the smoker and exposed class. This model gives us legitimate thought regarding the explanations for the spread of smoking in Bangladesh.

scholarly journals Analysis of a Model for Coronavirus Spread

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 820 ◽  
Author(s):  
Youcef Belgaid ◽  
Mohamed Helal ◽  
Ezio Venturino
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Global Stability ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Early Stage ◽  
Asymptomatic Individuals ◽  
Restrictive Measures ◽  
Disease Free

The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

scholarly journals Optimal Control for Transmission of Water Pollutants

2018 ◽  
Vol 3 (4) ◽  
pp. 381-391 ◽  
Author(s):  
Nita H. Shah ◽  
Shreya N. Patel ◽  
Moksha H. Satia ◽  
Foram A. Thakkar
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Waste Materials ◽  
Chemical Plants ◽  
Water Pollutants ◽  
Linear Ordinary Differential Equations ◽  
Oil Gas

Pollutants are formed when oil, gas, chemical plants, etc. discharge their harmful waste materials into stream or other water bodies. In this paper, a mathematical model for water pollutants which are soluble and insoluble has been formulated as a system of non-linear ordinary differential equations. Control is applied on insoluble water pollutants to process them into soluble water pollutants. Numerical simulation has been carried out which suggest that soluble water pollutants are increasing as compared to insoluble water pollutants.

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.

Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

2017 ◽  
Vol 10 (07) ◽  
pp. 1750096 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Yasir Khan ◽  
Taj Wali Khan ◽  
Saeed Islam
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For [Formula: see text], the disease-free equilibrium is stable both locally and globally and for [Formula: see text], the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.

scholarly journals Dynamical Analysis of a Mathematical Model of COVID-19 Spreading on Networks

2021 ◽  
Vol 8 ◽  
Author(s):  
Wang Li ◽  
Xinjie Fu ◽  
Yongzheng Sun ◽  
Maoxing Liu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Effective Strategies ◽  
Disease Spreading ◽  
Next Generation Matrix ◽  
Disease Free ◽  
The Basic Reproduction Number

In this article, an SEAIRS model of COVID-19 epidemic on networks is established and analyzed. Following the method of the next-generation matrix, we derive the basic reproduction number R0, and it shows that the asymptomatic infector plays an important role in disease spreading. We analytically show that the disease-free equilibrium E0 is asymptotically stable if R0≤1; moreover, the effects of various quarantine strategies are investigated and compared by numerical simulations. The results obtained are informative for us to further understand the asymptomatic infector in COVID-19 propagation and get some effective strategies to control the disease.

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