Browsing by Author "Bilge, Ayse Humeyra"

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Citation Count: 0
A Bicriteria Model to Determine Pareto Optimal Pulse Vaccination Strategies
(Wiley, 2024) Samanlıoğlu, Funda; Bilge, Ayşe Hümeyra; Karaca, Tolga Kudret; Bilge, Ayse Humeyra
The aim of this paper is to determine approximate Pareto optimal (efficient) pulse vaccination strategies for epidemics modeled by the susceptible-infected-removed (SIR) without population dynamics, characterized by a single epidemic wave. Pulse vaccination is the application of the vaccination campaign over a limited time interval, by vaccinating susceptible individuals at a constant vaccination rate. A pulse vaccination strategy includes the determination of the beginning date and duration of the campaign and the vaccination rate. SIR with vaccination (SIRV) epidemic model is applied during pulse vaccination campaign, resulting in final proportions of removed (Rf) and vaccinated (Vf) individuals at the end of the epidemic. The burden of the epidemic is estimated in terms of Rf and Vf; two criteria are simultaneously minimized: vaccination cost and treatment cost of infected individuals and other economic losses due to sickness that are assumed to be proportional to Vf and Rf, respectively. To find approximate efficient solutions to this bicriteria problem, ODE and genetic algorithm toolboxes of MATLAB are integrated (GA-ODE). In GA-ODE, an augmented weighted Tchebycheff program is used as the evaluation function, calculated by solving the SIRV model and obtaining Rf and Vf values. Sample approximate efficient vaccination strategies are determined for diseases with a basic reproduction number (R0) 1.2 to 2.0. Consequently, obtained strategies are characterized as short-period campaigns that start as early as possible, i.e., as soon as vaccines are available and the vaccination rate increases with the severity of the disease (R0) and the importance weight given to minimization of Rf.
Citation Count: 0
Dynamics of Feline Coronavirus and FIP: A Compartmental Modeling Approach
(Hindawi Ltd, 2023) Bilge, Ayşe Hümeyra; 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: 0
Epidemic Models for Chemical Gel Phase Transformation: Effect of Optical Measurements with Different Wavelengths
(Taylor & Francis Inc, 2023) Bilge, Ayşe Hümeyra; Bilge, Ayse Humeyra; Pekcan, Onder; Incegul, Metehan
In our previous work we characterized the sol-gel transition of chemical and physical gels in terms of epidemic models which describe the spread of a disease in a society. We have shown that gelation in chemical gels can be represented by the Susceptible-Infected-Recovered (SIR) model, while the gelation mechanism of physical gels can be represented by the Susceptible-Infected-Susceptible (SIS) model. These studies were based on optical measurements at a single wavelength. In the present work we studied the gelation mechanism for chemical gels obtained from experiments that have been carried out with acrylamide (AAm) and N,N0-methylenebis (acrylamide) (Bis) as base materials for chemical gel formation in water and with cross-linker. The transmitted light intensity was measured for various wavelengths from 440 nm to 690 nm during the gelation process. The data are modeled by the epidemic SIR process. The results indicate that the gelation processes obtained from the same Bis and water contents observed at different wavelengths obey different SIR models. This observation is explained by the scattering of light of different wavelengths depending on the sizes of the micro-gels formed.
Citation Count: 1
A Susceptible-Infectious (SI) model with two infective stages and an endemic equilibrium
(Elsevier, 2022) Bilge, Ayşe Hümeyra; 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: 1
Thornthwaite's Method for the Computation of the Water Balance
(Springer International Publishing Ag, 2022) Bilge, Ayşe Hümeyra; Bilge, Ayse Humeyra; Ulker, Duygu
Evapotranspiration is one of the crucial processes on water balance under the effect of meteorological and environmental factors and soil and vegetation characteristics. Thornhtwaite's method for the evaluation of the water balance at a given place is related to the temperature, precipitation data at monthly or daily intervals and on the information on the water holding capacity of the soil at that place. The method is based on equating the sum of evapotranspiration and runoff to the sum of precipitation and soil moisture. In Thornthwaite's method, most steps of the calculation are expressed by mathematical formulas but the values of the amount of water retained in the soil as a function of potential evapotranspiration (PE), for each value of the water holding capacity (WHC) of the soil are given by tables. In this paper we present an overview of the method and we present mathematical formulas that fit the data of the of these tables, to express the relation between water retained in soil and potential evapotranspiration (PE) for different water holding capacity (WHC).