Browsing by Subject "Local stability"

Now showing 1 - 5 of 5

Open Access
Analysis of a gene regulatory network model with time delay using the secant condition
(IEEE, 2016-10-04) Ahsen, M. E.; Özbay, Hitay; Nicolescu, Silviu-Iulian
A cyclic model for gene regulatory networks with time delayed negative feedback is analyzed using an extension of the so-called secant condition, which is originally developed for systems without time delays. It is shown that suf cient conditions obtained earlier for delay-independent local stability can be further improved for homogenous networks to obtain delay-dependent necessary and suf cient conditions, which are expressed in terms of the parameters of the Hill-type nonlinearity.
Open Access
Analysis of an epidemic model for transmitted diseases in a group of adults and an extension to two age classes
(Hacettepe University, 2020) Gölgeli, M.; Atay, Fatihcan M.
Infectious diseases are a serious problem for public health and spark the interest in interdisciplinary studies. In this paper, we present two mathematical models describing a possible scenario for infectious diseases. The first model considers the dynamics of the disease among adults and emphasizes the role of carriers in the SIR model and the second model assumes that the disease is transmitted to children by adults. We state the equilibria for each model and study the local stability of the equilibria. Furthermore, we perform simulations using a parameter set that explains the spread of a specific infectious disease (meningococcal disease) and interpret the possible cases of transmission via simulations.
Open Access
Analysis of an extended gene regulatory network model with time delay
(Institute of Applied Mathematics of Baku State University, 2023) Özturk, Dilan; Özbay, Hitay
This paper is concerned with the analysis of an extended gene regulatory network model with time delayed negative feedback. An extended model amounts to considering the unmodeled dynamics in the earlier Gene regulatory network (GRN) designs. Stability analysis of the extended model is further investigated with different design parameters. A local stability condition is derived for a model of extended GRN with time delay. Several numerical examples are given to illustrate the stability characteristics of the delayed extended GRN model and the results are compared with the benchmark homogeneous gene regulatory network.
Open Access
Correction to: Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy
(Springer, 2021-06-14) Bulut, H.; Gölgeli, M.; Atay, Fatihcan M.
Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARS-CoV-2 pandemic, individuals follow these measures with varying degrees of meticulousness, as the perceptions regarding the impending danger and the efficacy of the measures are not uniform within a population. In this paper, a compartmental mathematical model is presented that takes into account the importance of personal cautiousness (as evidenced, for example, by personal hygiene habits and carefully following the rules) during the COVID-19 pandemic. Two countries, Turkey and Italy, are studied in detail, as they share certain social commonalities by their Mediterranean cultural codes. A mathematical analysis of the model is performed to find the equilibria and their local stability, focusing on the transmission parameters and investigating the sensitivity with respect to the parameters. Focusing on the (assumed) viral exposure rate, possible scenarios for the spread of COVID-19 are examined by varying the viral exposure of incautious people to the environment. The presented results emphasize and quantify the importance of personal cautiousness in the spread of the disease.
Open Access
A secant condition for cyclic systems with time delays and its application to Gene Regulatory Networks
(IFAC, 2015) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. -I.
A stability condition is derived for cyclic systems with time delayed negative feedback. The result is an extension of the so-called secant condition, which is originally developed for systems without time delays. This extension of the secant condition gives a new local stability condition for a model of GRNs (Gene Regulatory Networks) under negative feedback. Stability robustness of homogenous networks is also investigated.