Special Issue "Numerical Simulation and Control for Disease"

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Biological Processes and Systems".

Deadline for manuscript submissions: closed (15 September 2021).

Special Issue Editors

Dr. Sunmi Lee
E-Mail Website
Guest Editor
Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Korea
Interests: mathematical modeling and numerical simulations of epidemiological systems with an emphasis on the use of optimal control theory, and computational stochastic modeling using agent-based models and network models in infectious diseases transmission dynamics
Prof. Dr. Yongkuk Kim
E-Mail Website
Co-Guest Editor
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
Interests: Mathematical modeling and computation in Biology, in particular, epidemiology and medical problems. Mathematical models include differential equations and related stochastic processes.

Special Issue Information

Emerging and re-emerging infectious diseases are posing serious problems. The immediate and effective implementation of control measures is of concern for public health officials all around the world. Many critical factors increase the potential risks of emerging and re-emerging infectious diseases. These critical factors include climate change related to global warming and people’s mobility, which facilitate the expansion of many infectious diseases and persistence in human populations. Due to the extremely complex nature of disease transmission dynamics, developing more accurate models has become challenging.

Mathematical modeling is a useful tool for studying the transmission dynamics and control of communicable human diseases. Various infectious diseases, such as influenza, measles, tuberculosis, Ebola, Zika, dengue, malaria, SARS-CoV, MERS-CoV, COVID 19, etc., have been analyzed using statistical and mathematical modeling and numerical simulations. In particular, the role of early interventions using statistical/mathematical modeling is critical for mitigating the spread of emerging and re-emerging infectious diseases. In addition, the assessment of the rapid prevention and efficient countermeasures is increasingly important for mitigating the morbidity and mortality impact of emerging or re-emerging infectious diseases, particularly on those individuals at the highest risk of developing severe disease. 

This Special Issue focuses on innovative mathematical modeling and numerical simulations for control of emerging and re-emerging infectious diseases and welcomes research articles dealing with all such aspects.

Dr. Sunmi Lee
Prof. Dr. Yongkuk Kim
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 papers will be 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. Processes is an international peer-reviewed open access monthly 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 2000 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

  • Emerging or re-emerging infectious diseases modeling;
  • Mathematical and statistical modeling;
  • Numerical methods and simulations;
  • Ordinary differential equations, partial differential equations, integro-differential equations;
  • Stochastic processes, network models, agent-based models;
  • Advanced and conventional optimal control methods;
  • Cost-effectiveness analysis of countermeasures and interventions.

Published Papers (5 papers)

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Research

Article
A Multi-Scale Model for the Spread of HIV in a Population Considering the Immune Status of People
Processes 2021, 9(11), 1924; https://doi.org/10.3390/pr9111924 - 27 Oct 2021
Viewed by 314
Abstract
A multi-scale mathematical model is proposed, seeking to describe the propagation of Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through unprotected sexual contact. The uses of antiretroviral therapy (ART) and therapeutic failure are [...] Read more.
A multi-scale mathematical model is proposed, seeking to describe the propagation of Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through unprotected sexual contact. The uses of antiretroviral therapy (ART) and therapeutic failure are considered to show how the rate of propagation and prevalence are affected. The model consists of a complex network modeling the interactions on the population scale, coupled with the immunological dynamics of each individual, which is modeled by a system of differential equations. The immunological model allows to observe some known facts from the literature, such as to control HIV infection in the immune system, it is necessary to reduce the probability of healthy CD4 T cells becoming infected or increase the probability at which cells of the specific cell response against HIV eliminate infected CD4 T cells. At the population level, it is shown that, to have a high prevalence, it is not necessary for the virus to spread rapidly at the beginning of the simulation time. Additionally, it is observed that a greater number of sexual partners induces higher HIV prevalence. Using ART in the immune system reduces the number of infected CD4 T cells and, consequently, helps to reduce the spread of infection at the population scale. An important result observed in simulations is that the average number of HIV carriers who abandon ART is greater than those who access it. The study adds to the available literature an original simulation model that describes the dynamics of HIV propagation in a population, considering the immune state of people within that population, and serves as a basis for future research involving more detailed aspects aiming for a model closest to reality. Full article
(This article belongs to the Special Issue Numerical Simulation and Control for Disease)
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Article
Mathematical Model of COVID-19 Transmission Dynamics in South Korea: The Impacts of Travel Restrictions, Social Distancing, and Early Detection
Processes 2020, 8(10), 1304; https://doi.org/10.3390/pr8101304 - 17 Oct 2020
Cited by 2 | Viewed by 1850
Abstract
The novel coronavirus disease (COVID-19) poses a severe threat to public health officials all around the world. The early COVID-19 outbreak in South Korea displayed significant spatial heterogeneity. The number of confirmed cases increased rapidly in the Daegu and Gyeongbuk (epicenter), whereas the [...] Read more.
The novel coronavirus disease (COVID-19) poses a severe threat to public health officials all around the world. The early COVID-19 outbreak in South Korea displayed significant spatial heterogeneity. The number of confirmed cases increased rapidly in the Daegu and Gyeongbuk (epicenter), whereas the spread was much slower in the rest of Korea. A two-patch mathematical model with a mobility matrix is developed to capture this significant spatial heterogeneity of COVID-19 outbreaks from 18 February to 24 March 2020. The mobility matrix is taken from the movement data provided by the Korea Transport Institute (KOTI). Some of the essential patch-specific parameters are estimated through cumulative confirmed cases, including the transmission rates and the basic reproduction numbers (local and global). Our simulations show that travel restrictions between the epicenter and the rest of Korea effectively prevented massive outbreaks in the rest of Korea. Furthermore, we explore the effectiveness of several additional strategies for the mitigation and suppression of Covid-19 spread in Korea, such as implementing social distancing and early diagnostic interventions. Full article
(This article belongs to the Special Issue Numerical Simulation and Control for Disease)
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Article
Resource Allocation in Two-Patch Epidemic Model with State-Dependent Dispersal Behaviors Using Optimal Control
Processes 2020, 8(9), 1087; https://doi.org/10.3390/pr8091087 - 02 Sep 2020
Cited by 1 | Viewed by 740
Abstract
A two-patch epidemic model is considered in order to assess the impact of virtual dispersal on disease transmission dynamics. The two-patch system models the movement of individuals between the two-patches using a residence-time matrix P, where P depends on both residence times [...] Read more.
A two-patch epidemic model is considered in order to assess the impact of virtual dispersal on disease transmission dynamics. The two-patch system models the movement of individuals between the two-patches using a residence-time matrix P, where P depends on both residence times and state variables (infected classes). In this work, we employ this approach to a general two-patch SIR model in order to investigate the effect of state dependent dispersal behaviors on the disease dynamics. Furthermore, optimal control theory is employed to identify and evaluate patch-specific control measures aimed at reducing disease prevalence at a minimal cost. Optimal policies are computed under various dispersal scenarios (depending on the different residence-time matrix configurations). Our results suggest there is a reduction of the outbreak and the proportion of time spent by individuals in a patch exhibits less fluctuations in the presence of patch-specific optimal controls. Furthermore, the optimal strategies for each patch differ depending on the type of dispersal behavior and the different infection rate in a patch. In all of our results, we obtain that the optimal strategies reduce the number of infections per patch. Full article
(This article belongs to the Special Issue Numerical Simulation and Control for Disease)
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Article
Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation
Processes 2020, 8(7), 782; https://doi.org/10.3390/pr8070782 - 04 Jul 2020
Viewed by 695
Abstract
A mathematical model composed of two non-linear differential equations that describe the population dynamics of CD4 T-cells in the human immune system, as well as viral HIV viral load, is proposed. The invariance region is determined, classical equilibrium stability analysis is performed by [...] Read more.
A mathematical model composed of two non-linear differential equations that describe the population dynamics of CD4 T-cells in the human immune system, as well as viral HIV viral load, is proposed. The invariance region is determined, classical equilibrium stability analysis is performed by using the basic reproduction number, and numerical simulations are carried out to illustrate stability results. Thereafter, the model is modified with a delay term, describing the time required for CD4 T-cell immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations. For the new model, equilibriums are determined, their local stability is examined, and results are studied by way of numerical simulation. Full article
(This article belongs to the Special Issue Numerical Simulation and Control for Disease)
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Article
A Two-Patch Mathematical Model for Temperature-Dependent Dengue Transmission Dynamics
Processes 2020, 8(7), 781; https://doi.org/10.3390/pr8070781 - 03 Jul 2020
Viewed by 1186
Abstract
Dengue fever has been a threat to public health not only in tropical regions but non-tropical regions due to recent climate change. Motivated by a recent dengue outbreak in Japan, we develop a two-patch model for dengue transmission associated with temperature-dependent parameters. The [...] Read more.
Dengue fever has been a threat to public health not only in tropical regions but non-tropical regions due to recent climate change. Motivated by a recent dengue outbreak in Japan, we develop a two-patch model for dengue transmission associated with temperature-dependent parameters. The two patches represent a park area where mosquitoes prevail and a residential area where people live. Based on climate change scenarios, we investigate the dengue transmission dynamics between the patches. We employ an optimal control method to implement proper control measures in the two-patch model. We find that blockage between two patches for a short-term period is effective in a certain degree for the disease control, but to obtain a significant control effect of the disease, a long-term blockage should be implemented. Moreover, the control strategies such as vector control and transmission control are very effective, if they are implemented right before the summer outbreak. We also investigate the cost-effectiveness of control strategies such as vaccination, vector control and virus transmission control. We find that vector control and virus transmission control are more cost-effective than vaccination in case of Korea. Full article
(This article belongs to the Special Issue Numerical Simulation and Control for Disease)
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