Dynamics and Control of HIV/AIDS in Cyprus Using Real Data

Abstract

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 $R_{0} \ge 1$, 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.