Mathematical model of an infectious disease

CALCOLO ◽  
1979 ◽  
Vol 16 (4) ◽  
pp. 399-414 ◽  
Author(s):  
G. I. Marchuk ◽  
L. N. Belykh
Keyword(s):  
Infectious Disease ◽  
Mathematical Model

scholarly journals A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

scholarly journals On a new conceptual mathematical model dealing the current novel coronavirus-19 infectious disease

2020 ◽  
Vol 19 ◽  
pp. 103510
Author(s):  
Anwarud Din ◽  
Kamal Shah ◽  
Aly Seadawy ◽  
Hussam Alrabaiah ◽  
Dumitru Baleanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Novel Coronavirus

INTERLEUKIN MATHEMATICAL MODEL OF AN IMMUNE SYSTEM

1995 ◽  
Vol 03 (03) ◽  
pp. 889-902 ◽  
Author(s):  
URSULA FORYS
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Basic Properties

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

scholarly journals The SIR Dynamic Model of Infectious Disease Transmission from the Viewpoint of a Chemical Engineer

2020 ◽  
Author(s):  
Cory Simon
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Dynamic Model ◽  
Catalytic Reaction ◽  
Disease Transmission ◽  
Catalyst Deactivation ◽  
Batch Reactor ◽  
Chemical Engineer ◽  
Infectious Disease Transmission

The classical Susceptible-Infectious-Recovered (SIR) mathematical model of the dynamics of infectious disease transmission resembles a dynamic model of a batch reactor carrying out an auto-catalytic reaction with catalyst deactivation.

scholarly journals A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2562
Author(s):  
Begoña Cantó ◽  
Carmen Coll ◽  
Maria Jesús Pagán ◽  
Joan Poveda ◽  
Elena Sánchez
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Transmitted Disease ◽  
Threshold Value ◽  
Direct Transmission ◽  
Indirect Transmission ◽  
Control Procedures

In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm.

scholarly journals Fleeing lockdown and its impact on the size of epidemic outbreaks in the source and target regions - a COVID-19 lesson

2020 ◽  
Author(s):  
Maria Vittoria Barbarossa ◽  
Norbert Bogya ◽  
Attila Dénes ◽  
Gergely Röst ◽  
Hridya Vinod Varma ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Minor Role ◽  
Epidemic Outbreak ◽  
Geographic Regions ◽  
A Minor

Abstract The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of seeding a large number of infections all at once in regions with otherwise small number of cases. In this work, we investigate the effect of fleeing on the size of an epidemic outbreak in the region under lockdown, and also in the region of destination. We propose a mathematical model that is suitable to describe the spread of an infectious disease over multiple geographic regions. Our approach is flexible to characterize the transmission of different viruses. As an example, we consider the COVID-19 outbreak in Italy. Projection of different scenarios shows that (i) timely and stricter intervention could have significantly lowered the number of cumulative cases in Italy, and (ii) fleeing at the time of lockdown possibly played a minor role in the spread of the disease in the country.

scholarly journals Awareness programs control infectious disease – Multiple delay induced mathematical model

2015 ◽  
Vol 251 ◽  
pp. 539-563 ◽  
Author(s):  
David Greenhalgh ◽  
Sourav Rana ◽  
Sudip Samanta ◽  
Tridip Sardar ◽  
Sabyasachi Bhattacharya ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Multiple Delay ◽  
Awareness Programs

Identification of biological models described by systems of nonlinear differential equations

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Sergey I. Kabanikhin ◽  
Olga I. Krivorotko
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Inverse Problems ◽  
Numerical Experiment ◽  
Mathematical Models ◽  
Tumor Cells ◽  
Nonlinear Differential Equations ◽  
Optimization Approach ◽  
Biological Models ◽  
Gradient Type

AbstractFour simple mathematical models of pharmacokinetic, competition between immune and tumor cells, infectious disease and tuberculosis epidemic are considered. An optimization approach for identification those models based on gradient type methods is introduced. Inverse problems are formulated in the form of an operator equation and then reduced to the minimization of the corresponding misfit functionals. The adjoint problems are used for the calculation of gradients. A mathematical model of competition between immune and tumor cells is considered numerically. The results of a numerical experiment are demonstrated.

scholarly journals The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics

2020 ◽  
Author(s):  
Cory Simon
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Dynamic Model ◽  
Chemical Kinetics ◽  
Disease Transmission ◽  
Dynamic Models ◽  
Catalyst Deactivation ◽  
Batch Reactor ◽  
Mitigation Strategies ◽  
Infectious Disease Transmission

The classic Susceptible-Infectious-Recovered (SIR) mathematical model of the dynamics of infectious disease transmission resembles a dynamic model of a batch reactor carrying out an auto-catalytic reaction with catalyst deactivation. By making this analogy between disease transmission and chemical reactions, chemists and chemical engineers can peer into dynamic models of infectious disease transmission used to forecast epidemics and assess mitigation strategies.

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