Modeling the Influence of Small-Scale Diffusion Perturbations on the Development of Infectious Diseases under Immunotherapy

The article proposes a modification of the mathematical model of the immunotherapy influence on the immune response dynamics taking into account small-scale diffusion perturbations. The solution of the corresponding singularly perturbed model problem with time-delay is reduced to a sequence of solutions without time-delay, for that representations of the required functions in the form of asymptotic series as disturbances of solutions of the corresponding degenerate problems are constructed. We present the results of numerical modeling that illustrate the influence of diffusion redistribution of active factors on the infectious disease dynamics in the conditions of immunotherapy. The decrease in the level of the maximum concentration of antigens in the locus of infection as a result of their diffusion redistribution is illustrated.

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MODELING SMALL-SCALE SPATIAL DISTRIBUTED INFLUENCES ON THE DYNAMICS OF INFECTIOUS DISEASE ON CONDITION OF PHARMACOTHERAPY

Journal of Numerical and Applied Mathematics ◽

10.17721/2706-9699.2020.1.01 ◽

2020 ◽

pp. 5-17

Author(s):

A. Ya. Bomba ◽

S. V. Baranovsky

Keyword(s):

Infectious Disease ◽

Time Delay ◽

Asymptotic Expansions ◽

Numerical Experiments ◽

Model Problem ◽

Maximum Level ◽

Small Scale ◽

Diffusion Redistribution

This paper proposes modification of the simplest model of the infectious disease in the conditions of pharmacotherapy taking into account influence of small-scale spatial distributed diffusion influences. The singular disturbed model problem with time-delay is reduced to a sequence of problems without time-delay for which the corresponding representations of the asymptotic expansions of solutions are constructed. We present the results of numerical experiments that characterize the influence of spatial distributed diffusion «redistributions» of infectious disease factors on the development of the process on condition of pharmacotherapy. The decrease in the maximum level of concentration of pathogenic antigens in the locus of infection due to their diffusion «redistribution» is illustrated.

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Modeling the dynamics of epidemics of infectious diseases under conditions of diffusion perturbations

Physico-mathematical modelling and informational technologies ◽

10.15407/fmmit2021.32.058 ◽

2021 ◽

pp. 58-63

Author(s):

Andrii Bomba ◽

Serhii Baranovsky

Keyword(s):

Infectious Disease ◽

Infectious Diseases ◽

Epidemic Model ◽

Numerical Experiments ◽

Model Problem ◽

Asymptotic Series ◽

Singularly Perturbed ◽

Sirs Epidemic Model ◽

Spatially Distributed ◽

Perturbed Model

The paper proposes a modification of the SIRS epidemic model to take into account the influence of diffusion perturbations on the dynamics of the spread of an infectious disease. A singularly perturbed model problem with delay is reduced to a sequence of problems without delay. The sought functions are represented in asymptotic series as perturbations of solutions of the corresponding degenerate problems. The results of numerical experiments illustrating the influence of spatially distributed diffusion redistributions on the spread of an infectious disease are presented.

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Haplotype Explorer: an infection cluster visualization tool for spatiotemporal dissection of the COVID-19 pandemic

G3 Genes|Genome|Genetics ◽

10.1093/g3journal/jkab126 ◽

2021 ◽

Author(s):

Tetsuro Kawano-Sugaya ◽

Koji Yatsu ◽

Tsuyoshi Sekizuka ◽

Kentaro Itokawa ◽

Masanori Hashino ◽

...

Keyword(s):

Functional Limitations ◽

Time Dependent ◽

Network Visualization ◽

Disease Dynamics ◽

Accession Number ◽

Haplotype Networks ◽

Virus Serotype ◽

Serotype 1 ◽

Cluster Visualization ◽

Infectious Disease Dynamics

Abstract Summary Many of software for network visualization are available, but existing software have not been optimized to infection cluster visualization, especially the current worldwide invasion of COVID-19 since 2019. To reach the spatiotemporal understanding of epidemics, we have developed Haplotype Explorer. In Haplotype Explorer, users can explore the network interactively with metadata like accession number, locations, and collection dates. Time dependent transition of the network can be exported as continuous sections for making a movie. Here, we introduce features and products of Haplotype Explorer, demonstrating time-dependent snapshots and a movie of haplotype networks inferred from total of 4,282 SARS-CoV-2 genomes. Abstract The worldwide eruption of COVID-19 that began in Wuhan, China in late 2019 reached 10 million cases by late June 2020. In order to understand the epidemiological landscape of the COVID-19 pandemic, many studies have attempted to elucidate phylogenetic relationships between collected viral genome sequences using haplotype networks. However, currently available applications for network visualization are not suited to understand the COVID-19 epidemic spatiotemporally due to functional limitations, that motivated us to develop Haplotype Explorer, an intuitive tool for visualizing and exploring haplotype networks. Haplotype Explorer enables to dissect epidemiological consequences via interactive node filters and provides the perspective on infectious disease dynamics depend on regions and time, such as introduction, outbreak, expansion, and containment. Here, we demonstrate the effectiveness of Haplotype Explorer by showing features and an example of visualization. The demo using SARS-CoV-2 genomes are available at https://github.com/TKSjp/HaplotypeExplorer/blob/master/Example/. There are several examples using SARS-CoV-2 genomes and Dengue virus serotype 1 E-genes sequence.

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Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model

Epidemics ◽

10.1016/j.epidem.2016.11.003 ◽

2018 ◽

Vol 22 ◽

pp. 56-61 ◽

Cited By ~ 44

Author(s):

Sebastian Funk ◽

Anton Camacho ◽

Adam J. Kucharski ◽

Rosalind M. Eggo ◽

W. John Edmunds

Keyword(s):

Infectious Disease ◽

Real Time ◽

Mechanistic Model ◽

Disease Dynamics ◽

Infectious Disease Dynamics

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A singularly perturbed model problem for numerical computation

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(96)00113-6 ◽

1996 ◽

Vol 76 (1-2) ◽

pp. 277-285 ◽

Cited By ~ 27

Author(s):

P.W. Hemker

Keyword(s):

Numerical Computation ◽

Model Problem ◽

Singularly Perturbed ◽

Perturbed Model

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Deep and Shallow Water Low-Speed Maneuvering Tests: Comparison Between Experimental and Simulation Results

Volume 7: Ocean Engineering ◽

10.1115/omae2016-54982 ◽

2016 ◽

Author(s):

Felipe Ribolla Masetti ◽

Pedro Cardozo de Mello ◽

Guilherme F. Rosetti ◽

Eduardo A. Tannuri

Keyword(s):

Mathematical Model ◽

Small Scale ◽

Shallow Waters ◽

Hydrodynamic Coefficients ◽

Low Speed ◽

Tunnel Model ◽

Oceanographic Research ◽

Simulation Results ◽

The University ◽

The Mathematical Model

This paper presents small-scale low-speed maneuvering tests with an oceanographic research vessel and the comparison with mathematical model using the real time maneuvering simulator developed by the University of São Paulo (USP). The tests are intended to verify the behavior of the vessel and the mathematical model under transient and low speed tests. The small-scale tests were conducted in deep and shallow waters, with a depth-draft ratio equal to 1.28, in order to verify the simulator ability to represent the vessel maneuverability on both depth conditions. The hydrodynamic coefficients used in the simulator model were obtained by CFD calculations and wind tunnel model tests carried out for this vessel. Standard turning circle and accelerating turn maneuvers were used to compare the experimental and numerical results. A fair agreement was achieved for shallow and deep water. Some differences were observed mainly in the initial phase of the accelerating turn test.

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Risk Causal Analysis of Traffic-Intensive Waters Based on Infectious Disease Dynamics

Journal of Marine Science and Engineering ◽

10.3390/jmse7080277 ◽

2019 ◽

Vol 7 (8) ◽

pp. 277

Author(s):

Yong-jun Chen ◽

Qing Liu ◽

Cheng-peng Wan

Keyword(s):

Infectious Disease ◽

Risk Factors ◽

Causal Model ◽

Cloud Model ◽

Rapid Development ◽

River Estuary ◽

Yangtze River Estuary ◽

Disease Dynamics ◽

Transmission Process ◽

Infectious Disease Dynamics

Accidents occur frequently in traffic-intensive waters, which restrict the safe and rapid development of the shipping industry. Due to the suddenness, randomness, and uncertainty of accidents in traffic-intensive waters, the probability of the risk factors causing traffic accidents is usually high. Thus, properly analyzing those key risk factors is of great significance to improve the safety of shipping. Based on the analysis of influencing factors of ship navigational risks in traffic-intensive waters, this paper proposes a cloud model to excavate the factors affecting navigational risk, which could accurately screen out the key risk factors. Furthermore, the risk causal model of ship navigation in traffic-intensive waters is constructed by using the infectious disease dynamics method in order to model the key risk causal transmission process. Moreover, an empirical study of the Yangtze River estuary is conducted to illustrate the feasibility of the proposed models. The research results show that the cloud model is useful in screening the key risk factors, and the constructed causal model of ship navigational risks in traffic-intensive waters is able to provide accurate analysis of the transmission process of key risk factors, which can be used to reduce the navigational risk of ships in traffic-intensive waters. This research provides both theoretical basis and practical reference for regulators in the risk management and control of ships in traffic-intensive waters.

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