In this paper, a nonlinear deterministic mathematical model of ordinary differential equations has been formulated to describe the transmission dynamics of HSV-II. The well-posedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproduction number that governs the disease transmission was obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease-free equilibrium and endemic equilibrium point of the model equation was established using the basic reproduction number. The results show that, if the basic reproduction is less than one then the solution converges to the disease-free steady-state and the disease-free equilibrium is locally asymptotically stable. On the other hand, if the basic reproduction number is greater than one the solution converges to endemic equilibrium point and the endemic equilibrium is locally asymptotically stable. Also, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of HSV-II. Finally, numerical simulations of the model equations are carried out using the software DE Discover 2.6.4 and MATLAB R2015b with ODE45 solver. The results of simulation show that treatment minimizes the risk of HSV-II transmission from the community and the stability of disease-free equilibrium is achievable when R0<1. Manuscript profile

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. Manuscript profile

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. Manuscript profile

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. Manuscript profile