Stochastic Dynamics in Computational and Mathematical Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 1001

Special Issue Editors


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Guest Editor
QSP Immuno-Oncology, Bristol-Myers Sqibb, New York, NY, USA
Interests: computational biology; mathematical control theory; mathematical modelling; modelling of epidemics; optimisation and control; partial differential equations; stochastic modelling

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Guest Editor
Department of Biomedical Sciences, Grand Valley State University, Allendale, MI, USA
Interests: mathematical biology

Special Issue Information

Dear Colleagues,

The Stochastic Dynamics in Computational and Mathematical Biology Special Issue of Mathematics aims to frame the issues raised in well-stirred approximation and data modeling and address them with improved stochastic approaches. This Special Issue combines new analytical and/or numerical mathematical methods and modeling algorithms alongside implementations of well-accepted, standard modeling technologies in emerging biological and applied science areas: immuno-science, infectious diseases, oncology, pharmacology and toxicology. Stochastic simulations have always been challenging over computational costs, hence algorithmic improvements should definitely be welcome along the way, and today it is very efficient in all aspects: temporal, spatio-temporal, and agent-based simulations. In biology and applied biological sciences, utilization of stochastic dynamics is highly emerging at an industrial scale. We seek papers that bring any of these aforesaid aspects, pushing the circle a little wider. Topics well-suited for this section include, but are not limited to:

  • Stochastic modeling in biology;
  • Stochastic differential equations;
  • Partial differential equations;
  • Stochastic control and jump diffusion;
  • Single cell gene regulatory network;
  • Gene on-off and cell-fate decisions;
  • Stress response and biological trade-offs;
  • Channel dynamics and neurophysics;
  • Mathematical immunology;
  • Theoretical immunology;
  • Mathematical oncology;
  • Tissue architecture and heterogeneity;
  • Multiscale modeling;
  • Tissue simulation for disease and therapeutics;
  • Pharmacokinetics and toxicokinetics;
  • Heterogeneous drug distribution. 

Dr. Tarunendu Mapder
Dr. Daniel Bergman
Guest Editors

Manuscript Submission Information

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Published Papers (1 paper)

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Research

15 pages, 4986 KiB  
Article
Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process
by Fehaid Salem Alshammari and Fahir Talay Akyildiz
Mathematics 2023, 11(18), 3876; https://doi.org/10.3390/math11183876 - 11 Sep 2023
Viewed by 587
Abstract
The worldwide data for COVID-19 for active, infected individuals in multiple waves show that traditional epidemic models with constant parameters are not able to capture this kind of disease behavior. We solved this major open mathematical problem in this report. We first consider [...] Read more.
The worldwide data for COVID-19 for active, infected individuals in multiple waves show that traditional epidemic models with constant parameters are not able to capture this kind of disease behavior. We solved this major open mathematical problem in this report. We first consider the disease transmission rate for the stochastic SIRVI epidemic model, which satisfies the mean-reverting Ornstein–Uhlenbeck (OU) process, and we propose a new stochastic SIRVI model. We then showed the existence and uniqueness of the global solution and obtained sufficient conditions for the persistent mean and exponential extinction of infectious disease, which have not been given before. In the second part, we derive a nonlinear system of differential equations for the time-dependent transmission rate from the deterministic SIRVI model and present an algorithm to compute the time-dependent transmission rate directly from the given active, infected individuals’ data. We then show that the time-dependent transmission obtained from and perturbed by the Ornstein–Uhlenbeck process could be represented after using a smoothing technique using a finite linear combination of a Gaussian radial basis function, which was obtained from our algorithm. This novel computer-assisted proof provides a theoretical basis for other epidemic models and epidemic waves. Finally, some numerical solutions of the stochastic SIRVI model are presented using COVID-19 data from Saudi Arabia and Austria. Full article
(This article belongs to the Special Issue Stochastic Dynamics in Computational and Mathematical Biology)
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