Dynamics of a Hybrid HIV/AIDS Model with Age-Structured, Self-Protection and Media Coverage

Abstract

Taking into account the effects of the heterogeneity of the population and media coverage on disease transmission, in this paper, a hybrid HIV/AIDS model with age-structure, self-protection awareness and media coverage is formulated, which is made up of five partial differential equations (PDEs) and one ordinary differential equation (ODE). We establish the existence of the solution associated with the hybrid system and prove that the solution is unique, bounded and positive utilizing the semigroup approach. Based on the basic reproduction number R0, the threshold dynamics of this model are rigorously investigated, that is, there always is a unique disease-free steady state E0 and it is globally stable when R01, that is, the disease dies out. Further, there exists a unique endemic steady state E* and it is locally stable when R0>1 and some additional technical conditions are met. In addition, the uniform persistence of this hybrid system is demonstrated for R0>1, which means that the disease remains at the endemic level for a long time, which is not discussed in other age-structured infectious disease articles. Numerical simulations are also given to explain the main theoretical results, which suggest that age variability is a non-negligible factor in HIV/AIDS transmission, that is, the moment and scale of HIV/AIDS outbreaks are diverse for people of different ages, and media coverage can encourage people to take steps to avoid potential infection and control the spread of the disease.

Keywords

• HIV/AIDS
• hybrid model of PDEs and ODE
• age and media coverage
• basic reproduction number
• stability and uniform persistence