HIV/AIDS is a serious health problem that continues to present a significant health concern in underdeveloped nations and may be mostly brought on via unprotected sex. This study is designed and analyzed using a dynamic modeling approach to investigate the dynamic of HIV/AIDS model with vertical transmission and the impact of knowledge on its treatment. Our proposed model exhibit disease free and the endemic equilibrium. The uniqueness and the exactness of the model were investigated and the basic reproduction number using next generation matrix was obtained, Stability analysis was also carried out. The model analysis shows that the disease free equilibrium is locally asymptomatically stable (LAS) when Ro < 1. Our research suggests that treatment and awareness campaigns, when combined with other crucial control measures, may help keep the HIV/AIDS virus from spreading.

COVID-19 pandemic is now increasing concern to authorities and public health officials. The study is aimed to investigate the impact of vaccination in the absence of media induced fear. In this research, analysis and simulation of a mathematical model of COVID-19 incorporated with media induced fear and vaccination was made, the total population is divided into 5 sub-population classes; Susceptible, Exposed, Infected, Quarantine and Recovery. The disease free and the endemic equilibrium of the model were carried out and the basic reproduction number was obtained using the next generation matrix. The stability analysis of the model was done and it was ascertained that the disease free equilibrium of the biological model is stable. Due to its efficiency and accuracy in handling nonlinear coupled ordinary differential equations, the homotopy perturbation method is applied to obtain the approximate solution of the mathematical model and the obtained results was simulated using the computation software Maple 18 to study the impact of vaccination in each compartment of the model when the media induced fear. The outcome of the simulation process were presented graphically and interpreted accordingly and it was discovered that in eradicating the spread of COVID-19 in a society where there is no fear, vaccination is an alternative and better measure. HIGHLIGHTS Model formulation with vaccination Stability analysis of the disease free equilibrium and endemic equilibrium Numerical simulation of the mathematical model using the homotopy perturbation method Analysis of the impact of vaccination in controlling the spread of COVID-19 in the absence of media induced fear GRAPHICAL ABSTRACT