$${ SI}$$ S I infection on a dynamic partnership network: characterization of $$R_0$$ R 0

Abstract

We model the spread of an (Susceptible Infectious) sexually transmitted infection on a dynamic homosexual network. The network consists of individuals with a dynamically varying number of partners. There is demographic turnover due to individuals entering the population at a constant rate and leaving the population after an exponentially distributed time. Infection is transmitted in partnerships between susceptible and infected individuals. We assume that the state of an individual in this structured population is specified by its disease status and its numbers of susceptible and infected partners. Therefore the state of an individual changes through partnership dynamics and transmission of infection. We assume that an individual has precisely ‘sites’ at which a partner can be bound, all of which behave independently from one another as far as forming and dissolving partnerships are concerned. The population level dynamics of partnerships and disease transmission can be described by a set of differential equations. We characterize the basic reproduction ratio using the next-generation-matrix method. Using the interpretation of we show that we can reduce the number of states-at-infection to only considering three states-at-infection. This means that the stability analysis of the disease-free steady state of an -dimensional system is reduced to determining the dominant eigenvalue of a matrix. We then show that a further reduction to a matrix is possible where all matrix entries are in explicit form. This implies that an explicit expression for can be found for every value of .

Gender asymmetry in concurrent partnerships and HIV prevalence

“…To this end, we use a previously introduced model for infection dynamics on a dynamic network that takes into account partnership formation and separation as well as demographic turnover (Leung et al, 2012, 2015). General analytical results for the spread of infections on networks have mainly been for static networks (e.g.…”

“…In this paper, we extended the model of (Leung et al, 2012, 2015) to a heterosexual population with a 1:1 sex ratio and a two-stage infectious disease. Concurrent partnerships are modeled by allowing a maximum number of partners that an individual can have at the same time; we call this number the partnership capacity.…”

“…We have previously derived explicit expressions for the degree distributions, partnership-based concurrency indices, basic reproduction number R 0 , and relative contribution of the acute stage to R 0 in terms of model parameters (Leung et al, 2012, 2015). The endemic prevalence is characterized implicitly as solution of a fixed point problem that can be computed numerically.…”

Examining the reservoir potential of animal species for $$\varvec{\textit{Leishmania infantum}}$$ Leishmania infantum infection

“…Minimizing the negative logarithm of (6), parameters β i j are estimated, and subsequently, the next generation matrix K = R i j is quantified as R i j = β i j /(γ j + μ j ) [11,34,35].…”

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

“…This is also what allows the fitted model to be used for the mathematical simulation of the contact network over time – it is theoretically guaranteed to vary stochastically around the observed network statistics (as long as the model is not degenerate). Other approaches to modeling epidemics on networks have been developed (Leung, Kretzschmar, and Diekmann 2015; Keeling and Rohani 2008), including applications that have used static ERGMs with a separately derived and estimated process for edge dynamics (Khan, Dombrowski, and Saad 2014). However, TERGMs provide the only integrated, principled framework for the estimation of network models from sampled data (Krivitsky and Morris 2017) and simulation of complex dynamic networks with theoretically justified methods for handling changes in population size and composition over time (Krivitsky et al 2011).…”