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Mathematics
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Statistical and Mathematical Modelling of Infectious Diseases
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Statistical and Mathematical Modelling of Infectious Diseases

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 4769

Special Issue Editors

Dr. Wangjian Zhang

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Guest Editor
Department of Medical Statistics, School of Public Health, Sun Yat-sen University, Guangzhou 510080, China
Interests: statistical modeling of infectious diseases and the health impact of environmental exposures
Dr. Zhicheng Du

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Guest Editor
Department of Medical Statistics, School of Public Health, Sun Yat-sen University, Guangzhou 510080, China
Interests: statistical modeling of infectious diseases; surveillance and early warning of infectious diseases
Dr. Ziqiang Lin

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Guest Editor
Department of Psychiatry, New York University School of Medicine, New York, NY 10016, USA
Interests: mathematical modeling; environmental exposure and health; artificial intelligence-assisted diagnosis; statistical method development

Special Issue Information

Dear Colleagues,

The COVID-19 pandemic has drawn great attention to the dynamics and control of major infectious diseases. Numerous mathematical and statistical models, including compartmental models, agent-based models, and generalized linear models, have been applied to investigate the epidemiological characteristics of certain infectious diseases, as well as the effects of non-pharmaceutical interventions. However, several gaps remain in the development and application of models. First, the process of disease transmission, prevention, and control is complex; thus, different compartments are established to represent different steps and procedures in the process for dynamic models. Previous studies on COVID-19 mainly focused on the effects of vaccination, isolation, and quarantine, while ignoring several other important interventions including testing policy, public health information campaigns, and fiscal measures. Additionally, the improved model performance and increased complexity have made mathematical and statistical modeling of infectious diseases a dilemma. It is hard to assume and/or estimate critical epidemiological parameters in such complex models that mimic the dynamic of chronic infectious diseases including HIV/AIDS and hepatitis due to the lack of routine real-time surveillance, as observed with COVID-19. Moreover, increased complexity also makes the analytic solutions or numerical simulations of optimized methods hard to properly incorporate into models to assess the cost-effectiveness of the interventions on outbreaks.

This Special Issue aims to unite a collection of articles that attempt to cope with the above issues in COVID-19 and other major infectious diseases-related modeling. However, articles covering other relevant topics within the scope of mathematical and statistical modeling of infectious diseases are also welcome.

Dr. Wangjian Zhang
Dr. Zhicheng Du
Dr. Ziqiang Lin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • infectious disease
  • epidemic models
  • COVID-19
  • intervention assessment
  • compartmental models

Published Papers (5 papers)

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Research

25 pages, 3002 KiB  
Article
Modeling the Propagation of Infectious Diseases across the Air Transport Network: A Bayesian Approach
by Pablo Quirós Corte, Javier Cano, Eduardo Sánchez Ayra, Chaitanya Joshi and Víctor Fernando Gómez Comendador
Mathematics 2024, 12(8), 1241; https://doi.org/10.3390/math12081241 - 19 Apr 2024
Viewed by 389
Abstract
The COVID-19 pandemic, caused by the SARS-CoV-2 virus, continues to impact the world even three years after its outbreak. International border closures and health alerts severely affected the air transport industry, resulting in substantial financial losses. This study analyzes the global data on [...] Read more.
The COVID-19 pandemic, caused by the SARS-CoV-2 virus, continues to impact the world even three years after its outbreak. International border closures and health alerts severely affected the air transport industry, resulting in substantial financial losses. This study analyzes the global data on infected individuals alongside aircraft types, flight durations, and passenger flows. Using a Bayesian framework, we forecast the risk of infection during commercial flights and its potential spread across an air transport network. Our model allows us to explore the effect of mitigation measures, such as closing individual routes or airports, reducing aircraft occupancy, or restricting access for infected passengers, on disease propagation, while allowing the air industry to operate at near-normal levels. Our novel approach combines dynamic network modeling with discrete event simulation. A real-case study at major European hubs illustrates our methodology. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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17 pages, 521 KiB  
Article
Optimal Social and Vaccination Control in the SVIR Epidemic Model
by Alessandro Ramponi and Maria Elisabetta Tessitore
Mathematics 2024, 12(7), 933; https://doi.org/10.3390/math12070933 - 22 Mar 2024
Viewed by 460
Abstract
In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible–vaccinated–infected–recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the [...] Read more.
In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible–vaccinated–infected–recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, we present the results from a simulation-based study employing a numerical implementation of the optimally controlled system through the forward–backward sweep algorithm. The baseline model considered incorporates parameters representative of typical values observed during the recent pandemic outbreak. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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25 pages, 609 KiB  
Article
Planar Bistable Structures Detection via the Conley Index and Applications to Biological Systems
by Junbo Jia, Pan Yang, Huaiping Zhu, Zhen Jin, Jinqiao Duan and Xinchu Fu
Mathematics 2023, 11(19), 4139; https://doi.org/10.3390/math11194139 - 30 Sep 2023
Viewed by 733
Abstract
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in two-dimensional dynamical systems are studied: one is two one-point attractors, another is a one-point attractor accompanied by a cycle attractor. By the Conley index theory, we [...] Read more.
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in two-dimensional dynamical systems are studied: one is two one-point attractors, another is a one-point attractor accompanied by a cycle attractor. By the Conley index theory, we prove that there exist other isolated invariant sets besides the two attractors, and also obtain the possible components and their configuration. Moreover, we find that there is always a separatrix or cycle separatrix, which separates the two attractors. Finally, the biological meanings and implications of these structures are given and discussed. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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18 pages, 2185 KiB  
Article
Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference
by Xuan Leng, Asad Khan and Anwarud Din
Mathematics 2023, 11(8), 1806; https://doi.org/10.3390/math11081806 - 11 Apr 2023
Cited by 1 | Viewed by 974
Abstract
When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to [...] Read more.
When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that Rs0>1, and it was noticed that, for Rs<1, the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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16 pages, 5235 KiB  
Article
Quantile Regression in Space-Time Varying Coefficient Model of Upper Respiratory Tract Infections Data
by Bertho Tantular, Budi Nurani Ruchjana, Yudhie Andriyana and Anneleen Verhasselt
Mathematics 2023, 11(4), 855; https://doi.org/10.3390/math11040855 - 07 Feb 2023
Viewed by 1427
Abstract
Space-time varying coefficient models, which are used to identify the effects of covariates that change over time and spatial location, have been widely studied in recent years. One such model, called the quantile regression model, is particularly useful when dealing with outliers or [...] Read more.
Space-time varying coefficient models, which are used to identify the effects of covariates that change over time and spatial location, have been widely studied in recent years. One such model, called the quantile regression model, is particularly useful when dealing with outliers or non-standard conditional distributions in the data. However, when the functions of the covariates are not easily specified in a parametric manner, a nonparametric regression technique is often employed. One such technique is the use of B-splines, a nonparametric approach used to estimate the parameters of the unspecified functions in the model. B-splines smoothing has potential to overfit when the number of knots is increased, and thus, a penalty is added to the quantile objective function known as P-splines. The estimation procedure involves minimizing the quantile loss function using an LP-Problem technique. This method was applied to upper respiratory tract infection data in the city of Bandung, Indonesia, which were measured monthly across 30 districts. The results of the study indicate that there are differences in the effect of covariates between quantile levels for both space and time coefficients. The quantile curve estimates also demonstrate robustness with respect to outliers. However, the simultaneous estimation of the quantile curves produced estimates that were relatively close to one another, meaning that some quantile curves did not depict the actual data pattern as precisely. This suggests that each district in Bandung City not only has different categories of incidence rates but also has a heterogeneous incidence rate based on three quantile levels, due to the difference in the effects of covariates over time and space. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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