Abstract: This study is carried out to describe the behaviour of vehicles flow on the road, in the presence of blocking effects. A non-linear three dimensional system of ordinary differential equations is used to describe vehicles flow on the road. The study classify total vehicles population on the road into three compartments as Free – Slow – Released vehicles. The formulated model is well-posed. The blocking free equilibrium point is globally asymptotically stable. Further, effects of blocking are described using concept of retardation number. That is, blocking effect decrease whenever retardation number is less than one and the blocking effects increase if retardation number is greater than one. تفاصيل المقالة

In the current study, a deterministic mathematical model of HIV and Cholera co-infection is developed to analyze the impact of treatments in the presence of diseases in the population. The model consists of nine classes of the human population and one class of bacteria population. The formulated model is mathematically well-posed and biologically meaningful. The reproduction number is employed to analyze the extinction or spreading of the disease in the population. it is observed that cholera has a positive impact on HIV patients and HIV also has a positive impact on cholera patients. A separate analysis of each infection model and co-infection model is presented. Further, the stability analysis of equilibrium points is included. Finally, numerical simulations are performed using Matlab software. The result of numerical simulations shows that early treatment is very powerful for clearing or controlling cholera within a specified period of time and supports HIV/AIDS patients to live more years. تفاصيل المقالة

In this paper, a deterministic mathematical model is formulated to study the dynamics of human population subjected to HIV/AIDSwith Herbal medicine and ART as treatments. The total population is divided into eight compartments. The existence, uniqueness, positivity, and boundedness of the solutions are shown. Both treatments have a positive impact on the reduction of viral load in the body. The stability analysis of equilibrium points are are done. Disease free equilibrium point is locally asymptotically stable if the reproduction number is less than unity and unstable for greater than unity. تفاصيل المقالة