A Generating Function Approach to HIV Transmission with Dynamic Contact Rates

Abstract

The basic reproduction number, R0, is often defined as the average number of infections generated by a newly infected individual in a fully susceptible population. The interpretation, meaning, and derivation of R0 are controversial. However, in the context of mean field models, R0 demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner, R0 has been proposed as a method for understanding the relative impact of public health interventions with respect to disease eliminations from a theoretical perspective. The use of R0 is made more complex by both the strong dependency of R0 on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions for R0 is that a single individual’s behavior is constant over time. In this paper we derive expressions for both R0 and probability of an epidemic in a finite population under the assumption that people periodically change their sexual behavior over time. We illustrate the use of generating functions as a general framework to model the effects of potentially complex assumptions on the number of transmissions generated by a newly infected person in a susceptible population. We find that the relationship between the probability of an epidemic and R0 is not straightforward, but, that as the rate of change in sexual behavior increases both R0 and the probability of an epidemic also decrease.

Strong influence of behavioral dynamics on the ability of testing and treating HIV to stop transmission

“…One possible direction for further research is extending the various dichotomized aspects of the model to polychotomous or continuous measures. For example, dichotomized episodic risk can be replaced by continuous risk volatility 17 20 . Another is incorporating important aspects of sexual behavior that are not included in the present model, such as long-term monogamous or semi-monogamous partnerships, temporal changes in insertive or receptive behavior 21 or temporal changes in condom use with different types of partners.…”

Recombination smooths the time-signal disrupted by latency in within-host HIV phylogenies

“…In the normal regime, the time to the next coalescent event is computed in the way described in [39]. During periods of bottlenecks that occur every B frequency days, the time to the next coalescent event is an Exponential random variable with rate [40].…”

“…In the normal regime, the time to the next coalescent event is computed in the way described in [39].…”

“…In Figure 3a, we see an example of a tree generated using only a linear-growth coalescent model that accounts for linear increase in genetic diversity from the time of infection [39]. This model captures the lengthening of external branches as the infection progresses that is observed in empirical within-host HIV phylogenies.…”

Preface

“…The role of human behaviour in epidemic progress is of current interest in epidemiology. Romero-Severson, Meadors and Volz [14] consider random changes in contact rates occurring at the individual level in long-lived infections, such as those caused by HIV, after a period of stable behaviour over which the contact rates remain constant. By using the generating function formalism and assuming exponentially distributed periods of stable behaviour, the authors the derive an expression for the random number of infections generated by newly-infected individuals, compute its expectation, i.e.…”