Browsing by Author "Dobie, Ayse Peker"

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Citation Count: 0
Dynamics of Feline Coronavirus and Fip: a Compartmental Modeling Approach
(Hindawi Ltd, 2023) Dobie, Ayse Peker; Bayrakal, Alper; Or, Mehmet Erman; Bilge, Ayse Humeyra
The investigation of infectious agents invading human and nonhuman populations represents a rich research domain within the framework of mathematical biology, captivating the interest of scientists across various disciplines. In this work, we examine the endemic equilibrium of feline coronavirus and feline infectious peritonitis by using a modified susceptible-infected-susceptible epidemiological model. We incorporate the concept of mutations from FCoV to FIP to enrich our analysis. We establish that the model, when subjected to reasonable parameter ranges, supports an endemic equilibrium wherein the FCoV group dominates. To demonstrate the stability of the equilibria under typical parameters and initial conditions, we employ the model SCF presented by Dobie in 2022 (Dobie, 2022). We ascertain that the equilibrium values reside within the interior domains of stability. Additionally, we displayed perturbed solutions to enhance our understanding. Remarkably, our findings align qualitatively with existing literature, which reports the prevalence of seropositivity to FCoV among stray cats (Tekelioglu et al. 2015, Oguzoglu et al. 2010, Pratelli 2008, Arshad et al. 2004).
Citation Count: 1
A Susceptible-Infectious (si) Model With Two Infective Stages and an Endemic Equilibrium
(Elsevier, 2022) Ahmetolan, Semra; Demirci, Ali; Bilge, Ayse Humeyra; Dobie, Ayse Peker
The focus of this article is on the dynamics of a 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. The infection is deadly and it has no cure. 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, and it is shown that the disease-free equilibrium is stable whereas all other equilibrium points are asymptotically stable for parameter ranges determined by certain inequalities. In addition, relations between the basic reproduction number of the disease and the basic reproduction number of each infectious stage are examined. Furthermore, the case where all newborns from infected mothers are also infected is analysed. For this type of vertical transmission, endemic equilibrium is asymptotically stable for certain parameter ranges. Finally, a special case which refers to the disease without vital dynamics is investigated and its exact solution is obtained. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Citation Count: 7
Susceptible-Infectious (sis) Model With Virus Mutation in a Variable Population Size
(Elsevier, 2022) Dobie, Ayse Peker
The complex dynamics of a contagious disease in which populations experience horizontal and vertical transmissions, size variation, and virus mutations are of considerable practical and theoretical interest. We model such a system by dividing a population into three distinct groups: susceptibles (S), C-infected (C) and F-infected (F), based on the Susceptible-Infectious-Susceptible (SIS) model. Once the individuals in the C-infected group recover from the disease, they gain no permanent immunity. The virus can mutate in the group C. When it does, the individuals become members of the F-infected group. The mutated virus causes a lethal and incurable disease with a high mortality rate. We discuss the model for two cases. For the first case, all the newborns from infected mothers develop the disease shortly after their birth. For the second case, there exist equal transmission rates and the C-infected population is lifelong infectious. Our analysis shows that both systems have positive solutions, and the first model possesses four equilibrium points, the trivial one (extinction of the species), C-free equilibrium (extinction of the ancestor virus) and two endemic equilibria of different properties. We identify the net population growth rates of the susceptible and C-infected groups for the existence of the equilibria of the first model. We define the conditions of parameters for which species extinction and endemic equilibria are locally asymptotically stable. We observe that bifurcation occurs at the C-free equilibrium. For the second model, we find that there is only one endemic equilibrium and it is always locally asymptotically stable. We also determine the region for the net population growth rates of the susceptible and F-infected groups for the existence of the endemic equilibrium.