MODELLING AND STABILITY ANALYSIS OF GONORRHEA TRANSMISSION MODEL WITH TREATMENT AND CONDOM EFFICACY

Abstract

A deterministic gonorrhea model is designed and used to study the dynamics of transmission of
gonorrhea disease. The positivity of the solution was determined to be positive with the positive
initial data; the invariant region was also determined to be positively invariant. In the absent of
disease, the disease free equilibrium point was determined and shown to be both locally and
globally asymptotically stable when the associated basic reproduction 0 R , is less than unity
.Furthermore, the model has a unique endemic equilibrium point which is locally and globally
asymptotically stable, whenever the basic reproduction is greater than unity. Sensitivity analyses
and numerical simulation carried out shows that increase in the effective contact rate, which is the
most sensitive parameter followed by progression rate from exposed class to the infected class and
the relative risk of an infected persons been infective increase the burden of the disease in the
community, while increase in condom efficacy, compliance of condom used and treatment of
gonorrhea infected individual will reduce the disease burden and so it has a significant impact in
controlling gonorrhea transmission in the community.