A Network Immuno-epidemiological Model of HIV and Opioid Epidemics

Severe Substance Abuse Disorder (commonly known as Addiction), and HIV individually claim many lives all over the world every year. But the spread of HIV is often due to intravenous drug usage, and drug usage by HIV positive people often lower their immunity and effectiveness of HIV medication. We look at HIV-Opioid Usage as a co-infection situation, and formulate a within-host model linked with a dynamic network model with demography, through epidemiological parameters. We show that disease free equilibrium exists and is stable, compute boundary equilibriums and show their stability and compute the basic reproduction numbers and invasion reproduction numbers for both the diseases.