Recent Advances in Mathematical Modeling of COVID-19 and Other Infectious Diseases

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 763

Special Issue Editors


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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

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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

Manuscript Submission Information

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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)

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Research

17 pages, 966 KiB  
Article
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 558
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 R0 and calculate the equilibrium point. Secondly, when [...] Read more.
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 R0 and calculate the equilibrium point. Secondly, when R0<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 R0>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 R0 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
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