arXiv subjects

Ayse Peker-Dobie

Publications and source records attributed to Ayse Peker-Dobie.

3 recordsLinked to original sources

arXiv2024

Hopf Bifurcation in a Generalized Goodwin Model with Delay

Goodwin's model is a cornerstone in the study of dynamical systems within macroeconomics, explaining the interaction between employment ratio and wage share in a closed economy. Analogous to predator-prey dynamics in mathematical economics, the Goodwin model, despite its simplicity, effectively captures the periodic behavior of state variables over specific time intervals. By relaxing the initial assumptions, the model can be adapted to account for more complex economic scenarios. In this article, we study a higher-dimensional extension of the Goodwin model that incorporates variable capacity utilization and capital coefficient alongside employment ratio and wage share. In particular instances, the wage share and employment rate equations decouple from the overall system. For these cases, by incorporating a delay effect in the Phillips curve, we demonstrate that while the equilibrium of the generalized system remains stable within certain parameter domains in the absence of delay, the introduction of delay can induce a Hopf bifurcation, leading to periodic oscillations. We analytically derive the critical delay parameter value that destabilizes the equilibrium point via a Hopf bifurcation.

math.DS↗

arXiv2020

What Can We Estimate from Fatality and Infectious Case Data using the Susceptible-Infected-Removed (SIR) model? A case Study of Covid-19 Pandemic

The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its spread. Since the earliest stages of this major pandemic, academics have done a huge amount of research in order to understand the disease, develop medication, vaccines and tests, and model its spread. Among these studies, a great deal of effort has been invested in the estimation of epidemic parameters in the early stage, for the countries affected by Covid-19, hence to predict the course of the epidemic but the variability of the controls over the course of the epidemic complicated the modeling processes. In this article, the determination of the basic reproduction number, the mean duration of the infectious period, the estimation of the timing of the peak of the epidemic wave is discussed using early phase data. Daily case reports and daily fatalities for ten countries over the period January 22, 2020 - April 18, 2020 are evaluated using the Susceptible-Infected-Removed (SIR) model. For each country, the SIR models fitting cumulative infective case data within 5% error are analysed. It is observed that the basic reproduction number and the mean duration of the infectious period can be estimated only in cases where the spread of the epidemic is over (for China and South Korea in the present case). Nevertheless, it is shown that the timing of the maximum and timings of the inflection points of the proportion of infected individuals can be robustly estimated from the normalized data. The validation of the estimates by comparing the predictions with actual data has shown that the predictions were realised for all countries except USA, as long as lock-down measures were retained.

q-bio.PE↗

arXiv2020

A New Susceptible-Infectious (SI) Model With Endemic Equilibrium

The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ($S$) and two different infectious groups ($I_1$ and $I_2$). Once infected, an individual becomes a member of one of these infectious groups which have different clinical forms of infection. In addition, during the progress of the illness, an infected individual in group $I_1$ may pass to the infectious group $I_2$ which has a higher mortality rate. In this study, positiveness of the solutions for the model is proved. Stability analysis of species extinction, $I_1$-free equilibrium and endemic equilibrium as well as disease-free equilibrium is studied. Relation between the basic reproduction number of the disease and the basic reproduction number of each infectious stage is examined. The model is investigated under a specific condition and its exact solution is obtained.

q-bio.PE↗