Analysis of the Asymptotic Behavior Solutions of Some Models of Epidemic Processes

Pertsev, N. V.

doi:10.17537/2013.8.21

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Высокая размерность модели обусловлена описанием структуры населения с помощью различных групп, отражающих социально-экономические, демографические и другие аспекты жизни индивидуумов. В основу модели положены работы [24,25] и их обобщение на случай высокой размерности [26]. ПЕРЦЕВ и др.…”

Section: высокоразмерная модель динамики распространения вич-инфекцииunclassified

“…Следуя [26], рассмотрим некоторый регион, взрослое население которого представим в виде групп индивидуумов S 1 , . .…”

Section: уравнения моделиunclassified

“…Нетрудно заметить, что Q * -неотрицательная матрица, а внедиагональные элементы матрицы H * не положительны. Обращаясь к структуре системы (101), (102), можно доказать следующий важный результат [26].…”

Section: частный случай модели и её положения равновесияunclassified

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Application of M-Matrices for the Study of Mathematical Models of Living Systems

Pertsev¹,

Pichugin²,

Pichugina³

2018

Math.Biol.Bioinf.

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Some results are presented of application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models studied are described by differential equations with several delays, including distributed delay, and by high-dimensional systems of differential equations. To study the stability of the equilibriums the linearization method is used. Emerging systems of linear differential equations have a specific structure of the right-hand parts, which allows to effectively use the properties of M-matrices. As examples, the results of studies of models arising in immunology, epidemiology and ecology are presented.

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Section: высокоразмерная модель динамики распространения вич-инфекцииunclassified

Section: уравнения моделиunclassified

Section: частный случай модели и её положения равновесияunclassified

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Application of M-Matrices for the Study of Mathematical Models of Living Systems

Pertsev¹,

Pichugin²,

Pichugina³

2018

Math.Biol.Bioinf.

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Mathematical modeling regulatory mechanisms of a viral infection caused by hepatitis D virus with taking into account co-infection and super-infection

Saidalieva

Hidirova

2019

J. Phys.: Conf. Ser.

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The purpose of this paper is to develop mathematical and computer models for the regulatory mechanisms of the interconnected activity between liver cells, the hepatitis B virus and hepatitis D virus molecular-genetic systems at hepatitis D infectious process. The paper draws the results made by using methods of quantitative and qualitative analyse of functional-differential equations. The paper concludes that the developed model which has oscillatory mode, chaotic regime and destructive changes that can be identified by chronic hepatitis D with intermittent crisis, with severe hepatitis D and liver cirrhosis. The paper provides a new mathematical and computer models which are able to describe hepatitis D regulatory mechanisms and to diagnose the infectious process course and predict the outcome of disease.

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Analysis of an Epidemic Mathematical Model Based on Delay Differential Equations

Pertsev

Loginov

Топчий

2020

J. Appl. Ind. Math.

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Analysis of the Asymptotic Behavior Solutions of Some Models of Epidemic Processes

Cited by 5 publications

References 15 publications

Application of M-Matrices for the Study of Mathematical Models of Living Systems

Application of M-Matrices for the Study of Mathematical Models of Living Systems

Mathematical modeling regulatory mechanisms of a viral infection caused by hepatitis D virus with taking into account co-infection and super-infection

Analysis of an Epidemic Mathematical Model Based on Delay Differential Equations

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