Axioms

Special Issue Editors

Prof. Dr. Nedyu Popivanov

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Guest Editor

1. Department of Mathematics and Informatics, University of Sofia, 1164 Sofia, Bulgaria
2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Interests: partial differential equations; boundary value problems; mixed type equations; mathematical analysis; special functions; fractional calculus; numerical modeling; asymptotic theory

Dr. Tsvetan D. Hristov

E-Mail Website
Guest Editor

Faculty of Mathematics and Informatics, University of Sofia, 1164 Sofia, Bulgaria
Interests: mixed-type partial differential equations; mathematical modeling

Special Issue Information

Dear Colleagues,

Mathematical modeling is a valuable tool in understanding the dynamics of infectious diseases (such as the coronavirus disease COVID-19). This involves using mathematical equations to represent the transmission and control of infectious diseases at the population level. The mathematical analysis of continuous models, the construction of their various time-discrete variants, and the solving of appropriate inverse problems are important tools for uncovering the behaviors over time of many crucial parameters that characterize the diseases’ dynamics. These models are essential for assessing the effectiveness of vaccination strategies, determining the best vaccination ages and target groups, and predicting future growth patterns of infectious diseases.

This Special Issue welcomes the submission of research and review articles that address the development of novel mathematical modeling and its applications.

Prof. Dr. Nedyu Popivanov
Dr. Tsvetan D. Hristov
Guest Editors

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Keywords

COVID-19
mathematical modeling
infectious diseases
population dynamics
integer-order models
fractional-order models
partial differential equations
ordinary differential equations
parameter identification methodologies
inverse problems
computer simulation

Published Papers (1 paper)

Research

17 pages, 958 KiB

Open AccessArticle

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

by Lidong Huang, Yue Xia and Wenjie Qin

Axioms 2024, 13(5), 309; https://doi.org/10.3390/axioms13050309 - 8 May 2024

Viewed by 111

Abstract

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number

R_{0}

and calculate the equilibrium point. Secondly, when [...] Read more.

R_{0}

and calculate the equilibrium point. Secondly, when

R_{0} < 1

, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When

R_{0} > 1

, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of

R_{0}

is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of COVID-19 and Other Infectious Diseases)

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Published Papers (1 paper)

Research

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