Version 1
: Received: 25 January 2024 / Approved: 26 January 2024 / Online: 26 January 2024 (09:38:06 CET)
How to cite:
Ilavská, I.; Malacká, Z. Nonlinear Differential Equation and SIS Epidemiological Model with a Time Delay Bounded by Two Positive Functions. Preprints2024, 2024011877. https://doi.org/10.20944/preprints202401.1877.v1
Ilavská, I.; Malacká, Z. Nonlinear Differential Equation and SIS Epidemiological Model with a Time Delay Bounded by Two Positive Functions. Preprints 2024, 2024011877. https://doi.org/10.20944/preprints202401.1877.v1
Ilavská, I.; Malacká, Z. Nonlinear Differential Equation and SIS Epidemiological Model with a Time Delay Bounded by Two Positive Functions. Preprints2024, 2024011877. https://doi.org/10.20944/preprints202401.1877.v1
APA Style
Ilavská, I., & Malacká, Z. (2024). Nonlinear Differential Equation and SIS Epidemiological Model with a Time Delay Bounded by Two Positive Functions. Preprints. https://doi.org/10.20944/preprints202401.1877.v1
Chicago/Turabian Style
Ilavská, I. and Zuzana Malacká. 2024 "Nonlinear Differential Equation and SIS Epidemiological Model with a Time Delay Bounded by Two Positive Functions" Preprints. https://doi.org/10.20944/preprints202401.1877.v1
Abstract
In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since
many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality.
The occurrence of infectious diseases in the population represents a serious health, social and economic problem.
There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.
Keywords
nonlinear differential equation with time delay; SIS model; epidemiological model; positive solution
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
