On Solvability of One Infinite System of Nonlinear Functional Equations in the Theory of Epidemics (original) (raw)

2020, Eurasian Mathematical Journal

The Eurasian Mathematical Journal (EMJ) publishes carefully selected original research papers in all areas of mathematics written by mathematicians, principally from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time the EMJ publishes survey papers. The EMJ publishes 4 issues in a year. The language of the paper must be English only. The contents of the EMJ are indexed in Scopus, Web of Science (ESCI), Mathematical Reviews, MathSciNet, Zentralblatt Math (ZMATH), Referativnyi Zhurnal-Matematika, Math-Net.Ru. The EMJ is included in the list of journals recommended by the Committee for Control of Education and Science (Ministry of Education and Science of the Republic of Kazakhstan) and in the list of journals recommended by the Higher Attestation Commission (Ministry of Education and Science of the Russian Federation).

3 Bulletin of Mathematical Biology manuscript No

2016

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a databased model prediction of the number of unobserved exposed individuals over very long times.

Some Characteristics and Classifications of Mathematical And Epidemic Models

Mathematical models are important basic tools in basic scientific research in many areas of biology, including physiology, ecology, evolution, toxicology, immunology, natural resource management, and conversation biology. Mathematical biology may sound like a narrow discipline, but it encompasses all of biology and virtually all of stress of mathematical sciences, including Statistic, Operational research and scientific computing. In this paper we investigate and discuss the characteristics and classificationsof mathematical and epidemic models.

Biomathematical analysis and extension of the new class of epidemic models proposed by Satsuma et al. (2004)

Applied Mathematics and Computation, 2005

The aim of this paper is to discuss the new class of epidemic models proposed by Satsuma et al., which are characterized by incidence rates which are nonlinearly dependent on the number of susceptibles as follows: infection rate (S, I) = g(S)I. By adding the biologically plausible constraint g 0 (S) > 0, we study the SIR and the SEIR models with vital dynamics with such infection rate, and results are done on the global asymptotic stability of the disease free and of the endemic equilibria, similarly to the ones of the classical models, also in presence of traditional and pulse vaccination strategies. Relaxing the constraint g 0 (S) > 0, we show that the epidemic system may exhibit multiple endemic equilibria.

Dynamical models of ecosystems and epidemics

Future Generation Computer Systems, 1989

Taking the charge of the Molokai conference literally, this paper discusses problems in ecology and epidemiology that represent grand scientific challenges. The areas that we will discuss are of fundamental scientific importance; they are also ones where the potential for supercomputing to have major impact is tremendous, but not yet realized.

Lyapunov Functions and Global Properties of SEIR Epidemic Model

The aim of this paper is to analyze an SEIR epidemic model in which prophylactic for the exposed individuals is included. We are interested in finding the basic reproductive number of the model which determines whether the disease dies out or persist in the population. The global attractivity of the disease-free periodic solution is obtained when the basic reproductive number is less than unity and the disease persist in the population whenever the basic reproductive number is greater than unity, i.e. the epidemic will turn out to endemic. The linear and non-linear Lyapunov function of Goh-Volterra type was used to establish the sufficient condition for the global stability of the model.

Epidemic Models on Attractors

2000

Models for epidemic processes on attractors are studied. Thresholds for disease persistence are computed and used in the study of the global behavior of solutions of simple epidemic process on chaotic attractors is illustrated.

A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics, 2020

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

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