2006/01/01 by Maia Martcheva, Sergei S. Pilyugin · 79 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Social Sciences · #Basic reproduction number #Bifurcation #Biology #Bistability #Coinfection #Demography #Dominance (genetics) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Human immunodeficiency virus (HIV) #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Nonlinear system #Physics #Statistical physics #Virology
paper · doi:10.1137/040619272
published in SIAM Journal on Applied Mathematics 66(3), 843-872 (Society for Industrial and Applied Mathematics)
crossref issued 2006/01/01 · crossref published 2006/01/01 · crossref published-print 2006/01/01 · openalex publication_date 2006/01/01 · crossref created 2006/03/14 · crossref deposited 2017/01/29 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
We investigate an epidemic model of two diseases. The primary disease is assumed to be a slowly progressing disease, and the density of individuals infected with it is structured by age since infection. Hosts that are already infected with the primary disease can become coinfected with a secondary disease. We show that in addition to the disease-free equilibrium, there exists a unique dominance equilibrium corresponding to each disease. Without coinfection there are no coexistence equilibria; however, with coinfection the number of coexistence equilibria may vary. For some parameter values, there exist two coexistence equilibria. We also observe competitor-mediated oscillatory coexistence. Furthermore, weakly subthreshold (which occur when exactly one of the reproduction numbers is below one) and strongly subthreshold (which occur when both reproduction numbers are below one) coexistence equilibria may exist. Some of those are a result of a two-parameter backward bifurcation. Bistability occurs in several regions of the parameter space. Despite the presence of coinfection, coexistence of the two diseases appears possible only for relatively small values of the reproduction numbers---for large values of the reproduction numbers the typical outcome of competition is the dominance of one of the diseases, including bistable dominance where the competition outcome is initial condition dependent.