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SUMMARY:Staged HIV transmission and treatment in a dynamic model with conc
urrency
DTSTART;VALUE=DATE-TIME:20180712T050000Z
DTEND;VALUE=DATE-TIME:20180712T052000Z
DTSTAMP;VALUE=DATE-TIME:20240619T113732Z
UID:indico-contribution-61-231@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Katharine Gurski (Howard University)\nHIV progressio
n studies have asserted three stages: acute infection\, chronic infection\
, and AIDS. We develop a model with three stages and include an infection
class with non-uniform Highly Active Anti-Retroviral Treatment leading to
viral suppression. Capturing the incidence rate of HIV in minority U.S. wo
men requires a model stratified by race/ethnicity and sexual behaviour in
addition to assumptions of assortative partner choice and concurrent relat
ionships. We include the effect of concurrency following the work of Watts
and May (1992\, Math. Biosciences) who in a simple deterministic model al
lowed for overlapping partnerships and infection from either a new sexual
partner or a longtime partner who was uninfected at the start of the partn
ership. This model was hampered by the assumption of a latent phase which
generated a non-autonomous system. We present a new autonomous determinist
ic model of the effect of concurrent sexual partnerships that allows for a
n analytical study of disease transmission. We incorporate the effect of
concurrency through the newly derived force of infection term in a mathema
tical model of the transmission of HIV through sexual contact in a populat
ion stratified by sexual behaviour and race/ethnicity. Time series analysi
s\, as well as parameter sensitivity analysis\, determine which strategy h
as the largest impact in the short and long term. Interventions focused on
encouraging chronically infected into viral suppression\, as well as inte
rventions focused on maintaining viral suppression have the largest impact
on the long term dynamics\, and the latter having the largest impact on t
he heterosexual community due to current racial disparity in treatment. Wh
ile reducing concurrency likelihood and duration positively impacts the lo
ng term dynamics\, left unchecked\, an increase in concurrency will signif
icantly raise the values of the endemic equilibrium.\n\nhttps://conference
s.maths.unsw.edu.au/event/2/contributions/231/
LOCATION:University of Sydney New Law School/--107
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/231/
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SUMMARY:Studying the effect of pre-exposure prophylaxis on the dynamics of
different populations susceptible to HIV
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UID:indico-contribution-61-265@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Renee Dale (Louisiana State University)\nPre-exposur
e prophylaxis is a useful method for the preventing the transmission of HI
V to susceptible individuals. What target population would provide the big
gest impact on HIV dynamics? To answer this question\, we present a differ
ential equation model stratified by behavioural risk and sexual activity.
Some susceptible individuals have higher rates of risky behaviour that inc
rease their chance of contracting the disease. Similarly\, infected indivi
duals with risky behaviours are at higher risk of transmitting the disease
to a susceptible individual. We further divide the infected population by
their diagnosis status. We define model parameters for both the urban cas
e\, or high-density sexual network\, and the national case\, or mixture of
low- and high-density sexual network. Our results indicate that the undia
gnosed high-risk infected group is the largest contributor to the epidemic
. Our model suggests that when pre-exposure prophylaxis is applied to the
susceptible populations\, its effectiveness extends outside of the group t
hat is taking the drug\, providing herd immunity. Our models suggest that
a strategy targeting the high-risk susceptible population would have the l
argest impact. We also find that such a protocol has similar effects for t
he national and the urban case\, despite the smaller sexual network found
in rural areas. To further analyze the effect of herd immunity and network
density\, we simulate our model using a random walk. The parameters are s
ummarized and reduced to include sexual contact rate\, behaviour riskiness
\, medication adherence\, and diagnosis rate. These parameters are describ
ed using probability distributions\, and the status of an individual at ea
ch iteration is determined by random draws from those distributions and a
control equation. Susceptible individualsâ€™ adherence to pre-exposure pro
phylaxis modifies their transmission risk term. We simulate under both urb
an and national network conditions\, as well as low-density or rural sexu
al network conditions. The effect of different adherence distributions is
also analyzed over varying proportions of susceptible individuals on pre-e
xposure prophylaxis medications. We hope this method will better illuminat
e the herd immunity effect provided by targeting high-risk susceptible ind
ividuals on different sexual networks.\n\nhttps://conferences.maths.unsw.e
du.au/event/2/contributions/265/
LOCATION:University of Sydney New Law School/--107
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/265/
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SUMMARY:Contribution of mass incarceration to HIV and optimal control of S
IR model
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DTEND;VALUE=DATE-TIME:20180712T060000Z
DTSTAMP;VALUE=DATE-TIME:20240619T113732Z
UID:indico-contribution-61-239@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Hem Joshi (Xavier University)\nWe develop a Suscepti
bles\, Infected and Recovered (SIR) type mathematical model of HIV epide
miology to explore a possible mechanism by which mass incarceration can le
ad to increased HIV incidence. The results are particularly relevant for t
he African American community in the United States that represents only 12
% of the total population but accounts for 45% of HIV diagnoses and 40% o
f the incarcerated population. While most explanations of the link betwee
n mass incarceration or anything else that leads to a population with a lo
w ratio of males to females and higher HIV burden are based on the complic
ated idea of sexual concurrency\, we propose a much simpler mechanism base
d on the idea of sexual activity compensation. The pool of men will increa
se their sexual activity to meet the demands of the female population. Th
rough mathematical analysis and numerical simulation\, we demonstrate that
these assumptions produce a situation in which mass incarceration lead t
o higher HIV incidence.\n\n\nWe also develop an optimal control model of S
IR type. In this model\, the control is education or information given t
o the public to manage a disease outbreak when effective treatments or va
ccines are not readily available or too costly to be widely used. We study
stability analysis and use optimal control theory on the system of differ
ential equations to achieve the goal of minimizing the infected population
. We illustrate our results with some numerical simulations.\n\nhttps://c
onferences.maths.unsw.edu.au/event/2/contributions/239/
LOCATION:University of Sydney New Law School/--107
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/239/
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