Mathematical modelling of hiv/aids transmission dynamics in a community with alcohol abuse problem

HIV is a major cause of preventable mortality in the world. Changes in behavior resulting from alcohol abuse are a risk factor for HIV transmission and progression. A compartmental mathematical model that describes the dynamics of HIV/AIDS transmission and progression in a community plagued with unhealthy alcohol consumption was formulated. Model analysis was done and it was found out that the disease-free equilibrium is globally asymptotically stable whenever the basic reproductive number is less than one. Also, the model was analyzed to provide both analytical and numerical solutions that answer the question of whether unhealthy alcohol consumption has any impact on HIV/AIDS transmission and progression. The results indicated that unhealthy alcohol consumption and its accompanying behaviors play a role in new HIV infections. Increasing alcohol abuse initiation rate by 10%, increases the basic reproductive number by 0.5%. A substantial number of new HIV infections are attributable to unhealthy alcohol use. However, an optimal control directed at alcohol abuse alone is not sufficient to reducing the number of HIV infections.