Browsing by Author "Hincal E."
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Item Dynamics and control of HIV/AIDS in cyprus using real data(Springer Verlag, 2019) Hincal E.; Sanlidag T.; Saad F.T.; Suer K.; Baba I.A.; Sayan M.; Kaymakamzade B.; Sultanoglu N.This article presents a mathematical model that studies the dynamics of HIV in North and South Cyprus. The global stability of the two equilibrium points involved are disease-free and endemic, and are performed using Lyapunov function. We have showed that the stability is dependent on the magnitude of the basic reproduction number R 0 . If R 0 < 1, the disease free equilibrium point is globally asymptotically stable and the disease vanishes, whereas if R 0 ≥ 1, the endemic equilibrium point is globally asymptotically stable and epidemics will occur. Real data obtained from the Turkish Republic of Northern Cyprus Ministry of Health is used to examine and predict the progress of HIV in North Cyprus, as well as comparing our results with South Cyprus using their published data. Reported HIV positive cases of only Turkish and Greek Cypriots were included from the data obtained from Turkish Republic of Northern Cyprus Ministry of Health and South Cyprus data, respectively. The results showed that, the basic reproduction number of North and South Cyprus are 0.00012 and 0.00034 respectively; which are less than one; hence, this indicates that there is currently no epidemic in the country. Furthermore, the number of HIV positive individuals in North Cyprus is likely to increase by almost 50%, whereas for South Cyprus an increase of 100% of the initial value (of 2017) is estimated in the next 20 years. Thus, the authorities should take the necessary actions and strategic measures for controlling the spread of the disease. © 2019, Springer Nature Switzerland AG.Item Global stability analysis of HIV+ model(Springer Verlag, 2019) Saad F.T.; Sanlidag T.; Hincal E.; Sayan M.; Baba I.A.; Kaymakamzade B.We developed and studied a mathematical model of HIV+. Two equilibriums points were found, disease free and endemic equilibrium, and basic reproduction ratio R 0 was also calculated by the use of next generation matrix. Global stability analysis of the equilibria was carried out by the use of Lyapunov function, and it was shown that the stability of the equilibria depends on the magnitude of the basic reproduction ratio. When R 0 < 1, the disease free equilibrium is globally asymptotically stable, and disease dies out. On the other hand if R 0 ≥ 1, the endemic equilibrium is globally asymptotically stable and epidemics occurs. Reported cases of 13646 HIV-1 positive were obtained in the year 2016 from Ministry of Health, Turkey (MOH). This data is used to present the numerical simulations, which supports the analytic result. R 0 was found to be 1.98998, which is bigger than 1, this shows the threat posed by HIV in Turkey. © 2019, Springer Nature Switzerland AG.Item Comparison of the Rate of Induced Intrinsic Pathway of Apoptosis on COLO-320 and COLO-741(Springer, 2021) Hincal E.; Soykut G.; Tijjani Saad F.; Vatansever S.; Abdullahi Baba I.; Çalış İ.; Kaymakamzade B.; Becer E.Mathematical modeling is a key tool in understanding complicated behavior of large signal transduction networks. In this paper a mathematical model is developed to understand the complex signaling behavior of induced apoptosis in Colo-320 and Colo-741 cell lines. The model studies the intrinsic pathway of apoptosis induced by Apaf-1, Cyt-c, and Caspase 3. Experimentally these tests were carried out five times for three groups; namely Control, DCM and Aqueous groups. The main aim is to compare the rate of the occurrence of apoptosis in the two cells Colo-320 and Colo-741 using experimental data. Numerical results reveal that apoptosis takes place at the same time in DCM for Colo-320 and Colo-741, but slightly faster in Aqueous group for Colo-320. It was observed that it took place between the 5–7th h in all the cases. © 2021, Springer Nature Switzerland AG.Item Trends and Risk of HIV/AIDS in Turkey and Its Cities(Springer, 2021) Hincal E.; Sayan M.; Kaymakamzade B.; Şanlidağ T.; Sa’ad F.T.; Baba I.A.We developed a mathematical model to study the dynamics of HIV/AIDS in Turkey and its environs. Two equilibrium points were found and local stability analysis of the equilibria was conducted. It was found that the stability of the equilibria depend on a threshold quantity; the basic reproduction ratio R0. When R0≤ 1, the disease free equilibrium is locally asymptotically stable and disease dies out. When R0≥ 1, the endemic equilibrium is locally asymptotically stable and disease persist. We considered the dynamics of the disease in 25 cities of Turkey and found out that the basic reproduction ratio for 17 cities is greater than one, while 8 of them have less than one. This indicates there is going to be epidemics in these 17 cities and the disease will die out in the remaining cities. The results also indicated that some of the cities (with bigger basic reproduction ratio) are at bigger risk than the others. There is need for quick intervention by the relevant authorities, especially in the cities with greater risk of the disease. © 2021, Springer Nature Switzerland AG.