Open AccessThe dynamics of a simple, risk-structured HIV model
Author(s) -
Mark Kot,
Dobromir Dimitrov
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020232
Subject(s) - basic reproduction number , mathematics , eigenvalues and eigenvectors , population , complement (music) , stability (learning theory) , stability theory , separable space , constant (computer programming) , simple (philosophy) , mixing (physics) , variance (accounting) , econometrics , statistics , mathematical economics , demography , biology , computer science , economics , mathematical analysis , physics , nonlinear system , genetics , philosophy , sociology , accounting , epistemology , quantum mechanics , machine learning , programming language , complementation , gene , phenotype
Many diseases, such as HIV, are heterogeneous for risk. In this paper, we study an infectious-disease model for a population with demography, mass-action incidence, an arbitrary number of risk classes, and separable mixing. We complement our general analyses with two specific examples. In the first example, the mean of the components of the transmission coefficients decreases as we add more risk classes. In the second example, the mean stays constant but the variance decreases. For each example, we determine the disease-free equilibrium, the basic reproduction number, and the endemic equilibrium. We also characterize the spectrum of eigenvalues that determine the stability of the endemic equilibrium. For both examples, the basic reproduction number decreases as we add more risk classes. The endemic equilibrium, when present, is asymptotically stable. Our analyses suggest that risk structure must be modeled correctly, since different risk structures, with similar mean properties, can produce different dynamics.