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Mathematics
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Advances of Numerical Methods for Dynamical Systems
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Advances of Numerical Methods for Dynamical Systems

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 1534

Special Issue Editor

Prof. Dr. Suares Clovis Oukouomi Noutchie

E-Mail Website
Guest Editor
Department of Mathematics and Applied Mathematics, North-West University, Mmabatho 2735, South Africa
Interests: applied mathematics; dynamical systems; difference equations

Special Issue Information

Dear Colleague,

The theory of dynamical systems finds applications in a wide variety of fields, such as mathematics, engineering, physics, biology, chemistry, economics, and social sciences. Evolution equations governing dynamical systems in general do not admit analytic solutions. Reliable numerical schemes are, therefore, needed to approximate solutions and investigate the asymptotic behavior of complex evolutionary systems.

This Special Issue aims to publish original high-quality research articles on advanced numerical methods for dynamical systems.

The Special Issue plans to accept papers utilizing numerical tools to simulate dynamical systems occurring in natural processes and engineering. The evolution equations of interest include difference equations, ordinary differential equations, partial differential equations, stochastic differential equations, and fractional differential equations.

Prof. Dr. Suares Clovis Oukouomi Noutchie
Guest Editor

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

  • numerical analysis
  • dynamical systems
  • ordinary differential equations
  • partial differential equations
  • stochastic differential equations
  • fractional differential equations

Published Papers (1 paper)

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Research

17 pages, 1122 KiB  
Article
Modelling the Influence of Dynamic Social Processes on COVID-19 Infection Dynamics
by Farai Nyabadza, Josiah Mushanyu, Rachel Mbogo and Gift Muchatibaya
Mathematics 2023, 11(4), 963; https://doi.org/10.3390/math11040963 - 13 Feb 2023
Viewed by 1180
Abstract
Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread, especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave had subsequent waves of COVID-19 infections. In this [...] Read more.
Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread, especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave had subsequent waves of COVID-19 infections. In this study, we develop a deterministic model for COVID-19 that includes dynamic non-pharmaceutical interventions known as social dynamics with the goal of simulating the effects of dynamic social processes. The model steady states are determined and their stabilities analysed. The model has a disease-free equilibrium point that is locally asymptotically stable if R0<1. The model exhibits a backward bifurcation, implying that reducing the reproduction number below one is not sufficient for the elimination of the disease. To ascertain the range of parameters that affect social dynamics, numerical simulations are conducted. The only wave in South Africa in which interventions were purely based on human behavior was the first wave. The model is thus fitted to COVID-19 data on the first wave in South Africa, and the findings given in this research have implications for the trajectory of the pandemic in the presence of evolving societal processes. The model presented has the potential to impact how social processes can be modelled in other infectious disease models. Full article
(This article belongs to the Special Issue Advances of Numerical Methods for Dynamical Systems)
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