Browsing by Author "Baba I.A."
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Item Dynamics of HIV/AIDS in Turkey from 1985 to 2016(Springer Netherlands, 2018) Sayan M.; Hınçal E.; Şanlıdağ T.; Kaymakamzade B.; Sa’ad F.T.; Baba I.A.In this paper, we formulated a mathematical model that studies the dynamics of HIV/AIDS in Turkey from 1985 to 2016. We find two equilibrium points, disease free equilibrium and endemic equilibrium. Global stability analysis of the equilibria was conducted using Lyapunov function which depends on the basic reproduction ratio R0. If R0 < 1, the disease free equilibrium point is globally asymptotically stable, and if R0 ≥ 1 the endemic equilibrium point is globally asymptotically stable. We computed and predicted the basic reproduction ratios across all the years. It was found out that there were flaws in the exact values of R0 which is related to the poor registration system of HIV/AIDS in Turkey. Hence, there is need for the government to improve the system in order to cover the actual cases of the disease. The increase of the basic reproduction ratio over the years also shows the need for the relevant authorities to adopt appropriate control measures in combating the disease. © 2017, Springer Science+Business Media B.V.Item Role of awareness in controlling HIV/AIDS: a mathematical model(Springer Netherlands, 2018) Kaymakamzade B.; Şanlıdağ T.; Hınçal E.; Sayan M.; Sa’ad F.T.; Baba I.A.This paper proposes and analyzes two epidemic models incorporating the effects of the awareness programs. One of the models is for HIV awareness and the other AIDS awareness. Awareness programs play a promising role in disseminating the information about outbreak of any HIV/AIDS in Turkey. This motivates people to take precautionary measures and guides the infected individuals to get the required treatment. The aim of this study is to investigate the impact of the awareness on the spread and control of HIV/AIDS in Turkey. The models are analyzed using stability theory of differential equations. The sensitivity of parameters has been discussed and it has been found that the awareness education programs have positive impact in reducing the infection prevalence of the infective population in Turkey. © 2017, Springer Science+Business Media B.V.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 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.