Bifurcation analysis of vertical transmission model with preventive strategy

We formulate and analyze a deterministic mathematical model for the prevention of a disease transmitted horizontally and vertically in a population of varying size. The model incorporates prevention of disease on individuals at birth and adulthood and allows for natural recovery from infection. The main aim of the study is to investigate the impact of a preventive strategy applied at birth and at adulthood in reducing the disease burden. Bifurcation analysis is explored to determine existence conditions for establishment of the epidemic states. The results of the study showed that in addition to the disease-free equilibrium there exist multiple endemic equilibria for the model reproduction number below unity. These results may have serious implications on the design of intervention programs and public health policies. Numerical simulations were carried out to illustrate analytical results.