Running wave analysis of pandemic dynamics: a mathematical model.
https://doi.org/10.21683/1729-2646-2025-25-2-33-38
Abstract
This paper examines pandemic dynamics using running-wave-based tools and mathematical models. By extending the classic SIR (Susceptible-Infected-Removed) model to include spatial dependence, we explore how disease waves spread across a population. Through mathematical analysis and inference, we derive equations for the wave velocity and assess the severity of epidemics. Our findings emphasise the crucial role of reducing the contact factor in slowing the spread of a disease and minimising its consequences. The study highlights the power of mathematical modelling in understanding and responding to pandemics, suggesting insights into effective intervention strategies.
About the Authors
T. Asraa
Belgorod State National Research University
Russian Federation
Russian Federation
Taha Asraa, Postgraduate Student, Department of Mathematics and Software in Information Systems
I. S. Konstantinov
Belgorod State Technological University
Russian Federation
Russian Federation
Igor S. Konstantinov, Candidate of Engineering, Professor, Institute of Energy, Computer Science, and Control Systems
D. N. Starchenko
Belgorod State Technological University
Russian Federation
Russian Federation
Denis N. Starchenko , Candidate of Engineering, Associate Professor, Institute of Energy, Computer Science, and Control Systems
References
1. Nazneen S., King Abia A.L., Madhav S, editors. Emerging Pandemics: Connections with Environment and Climate Change (1st ed.). CRC Press; 2023.
2. Schulz S., Pastor R., Koyuncuoglu C. et al. Real-time Dissection and Forecast of Infection Dynamics during a Pandemic. 2023. (accessed 31.03.2025). Available at: https://www.researchgate.net/publication/369095299_Real-time_Dissection_and_Forecast_of_Infection_Dynamics_during_a_Pandemic.
3. Frutos R. Chapter 15 – Emergence and dynamics of COVID-19 and future pandemics. In: Barh D., editor. Omics approaches and technologies in COVID-19. Academic Press; 2023. Pp. 245-254.
4. Abiodun O., Olukayode A., Ndako J. Mathematical Modeling and Its Methodological Approach: Application to Infectious Disease. In: 2023 International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG). Omu-Aran; Nigeria. 2023. Pp. 1-14.
5. Bogdanov A.I., Mongush B.S., Kuzmin V.A., Orekhov D.A., Nikitin G.S., Baryshev A.N., Aidiev A.B., Gulyukin E.A. Analysis of models of the mathematical theory of epidemics and recommendations on the use of deterministic and stochastic models. Legal regulation in veterinary medicine 2022;(4):37-42. (in Russ.)
6. Piqueira J. R. C. Editorial: Epidemic models on networks. Frontiers in Physics. Sec. Social Physics 2022;10:1122070.
7. Cifuentes-Faura J., Faura-Martínez U., Lafuente-Lechuga M. Mathematical Modeling and the Use of Network Models as Epidemiological Tools. Mathematics 2022;10(18):3347. DOI: 10.3390/math10183347.
8. Alam N. An analytical technique to obtain traveling wave solutions to nonlinear models of fractional order. Partial Differential Equations in Applied Mathematics 2023;8:100533.
9. Zhang Q., Wu S.-L. Wave propagation of a discrete SIR epidemic model with a saturated incidence rate. Int. J. Biomath 2019;12:1950029. DOI: 10.1142/S1793524519500293.
10. Yin Zhang Y., Xiong J., Mao N. Epidemic model of Covid-19 with public health interventions consideration: a review. Authorea 2023. DOI: 10.22541/au.168539048.84429551/v1.
11. Department of Continuing Education, University of Oxford. 2021. The Pandemic Dynamics Series: Dr. Tom Crawford. (accessed 03/31/2025). Available at: https://www.conted.ox.ac.uk/profiles/tom-crawford
Review
For citations:
Asraa T., Konstantinov I.S., Starchenko D.N. Running wave analysis of pandemic dynamics: a mathematical model. Dependability. 2025;25(2):33-38. (In Russ.) https://doi.org/10.21683/1729-2646-2025-25-2-33-38
Views:
97
ISSN 1729-2646 (Print)
ISSN 2500-3909 (Online)
ISSN 2500-3909 (Online)
Email this article 