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SUMMARY:Optimal control with multiple human papillomavirus vaccines
DTSTART;VALUE=DATE-TIME:20180709T013000Z
DTEND;VALUE=DATE-TIME:20180709T020000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-42@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Tufail Malik (Merck & Co.\, Inc.\, USA)\nMany human
papillomavirus (HPV) vaccination programs currently administer three vacci
nes - a bivalent\, a quadrivalent and a nonavalent vaccine - for a two-dos
e course. In this talk a model will be presented to explore optimal vaccin
ation strategies using the three vaccines\, which differ in protection bre
adth\, cross-protection\, and type-specific efficacy. Assuming the HPV inf
ection prevalence in the population under the constant vaccination regime\
, optimal control theory will be used to discuss optimal vaccination strat
egies for the associated non-autonomous model when the vaccination rates a
re functions of time. The impact of these strategies on the number of infe
cted individuals and the accumulated cost will be assessed and compared wi
th the constant control case. Switch times from one vaccine combination to
a different combination including the nonavalent vaccine will be assessed
during an optimally designed HPV immunization program.\n\nhttps://confere
nces.maths.unsw.edu.au/event/2/contributions/42/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/42/
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SUMMARY:Mathematics of climate change and malaria transmission dynamics
DTSTART;VALUE=DATE-TIME:20180709T010000Z
DTEND;VALUE=DATE-TIME:20180709T013000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-66@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Abba Gumel (Arizona State University)\nClimate chang
e is known to significantly affect the dynamics of vector-borne diseases\,
such as malaria. In particular\, the species involved in the transmissio
n dynamics of malaria are affected by various abiotic conditions\, such as
temperature\, precipitation\, humidity and vapor pressure . A number of m
odels\, typically statistical (using data and statistical approaches to co
rrelate some climate variables with malaria incidence) or mechanistic (acc
ounting for the detailed dynamic nonlinear processes involved in disease t
ransmission)\, have been employed to assess the likely impact of anthropog
enic climate change on malaria transmission dynamics and control. These m
odels have (generally) reached divergent conclusions\, with some predictin
g a large expansion in the continental land area suitable for transmission
and in the number of people at risk of malaria\, while others predict onl
y modest poleward (and altitudinal) shifts in the burden of disease\, with
little net effect\, and the issue remains unresolved thus far. I will di
scuss some of our recent results on modelling the effect of climate variab
les (notably temperature) on the dynamics of malaria vector and disease.\n
\nhttps://conferences.maths.unsw.edu.au/event/2/contributions/66/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/66/
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SUMMARY:Mathematics of a sex-structured model for Syphilis transmission dy
namics
DTSTART;VALUE=DATE-TIME:20180709T020000Z
DTEND;VALUE=DATE-TIME:20180709T023000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-68@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Oluwaseun Sharomi (Khalifa University of Science and
Technology)\nSyphilis\, a major sexually-transmitted disease\, continues
to pose major public health burden in both under-developed and developed n
ations of the world. This study presents a new two-group sex-structured mo
del for assessing the community-level impact of treatment and condom use o
n the transmission dynamics and control of syphilis. Rigorous analysis of
the model shows that it undergoes the phenomenon of backward bifurcation.
In the absence of this phenomenon (which is shown to arise due to the re-i
nfection of recovered individuals)\, the disease-free equilibrium of the m
odel is shown to be globally-asymptotically stable (GAS) when the associat
ed reproduction number is less than unity. Furthermore\, the model can hav
e multiple endemic equilibria when the reproduction threshold exceeds unit
y. Numerical simulations of the model\, using data relevant to the transmi
ssion dynamics of the disease in Nigeria\, show that\, with the assumed 80
% condom efficacy\, the disease will continue to persist (i.e.\, remain en
demic) in the population regardless of the level of compliance in condom u
sage by males. Furthermore\, detailed optimal control analysis (using Pont
raygin's Maximum Principle) reveals that for situations where the cost of
implementing the controls (treatment and condom-use) considered in this st
udy is low\, channeling resources to a treatment-only strategy is more eff
ective than channeling them to a condom-use only strategy. Furthermore\, a
s expected\, the combined condom-treatment strategy provides a higher popu
lation-level impact than the treatment-only strategy or the condom-use onl
y strategy. When the cost of implementing the controls is high\, the three
strategies are essentially equally as ineffective.\n\nhttps://conferences
.maths.unsw.edu.au/event/2/contributions/68/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/68/
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SUMMARY:Global stability of some continuous and nonstandard discretization
models for the Ebola virus disease with fast and slow transmissions
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DTEND;VALUE=DATE-TIME:20180709T063000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-122@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Jean Lubuma (University of Pretoria)\nMathematical m
odels for the Ebola Virus Disease (EVD) were\, until recently\, mostly bas
ed on the fast/direct transmission route\, which involves contact with blo
od or body fluid and objects that have been contaminated by body fluid. Th
e fact that in almost all outbreaks of the EVD in Africa\, the index case
became infected through contact with infected animals\, such as fruit bats
and primates\, makes the environment a no negligible channel for slow/ind
irect transmission of the disease. \n\nIn this talk\, we incorporate both
direct and indirect transmission routes in the setting of SIR-type models
that are developed gradually. Firstly\, we add two compartments (for dead
individuals and for the environment) in order to capture infection through
the manipulation of deceased individuals before burial as well as contami
nated environment. Secondly\, we enrich the first model with self-protecti
on measures reflected by the addition of classes of vaccinated and trained
individuals. \n\nFor the two models\, we prove that the disease-free equi
librium is globally asymptotically stable (GAS) whenever the basic reprodu
ction number is less than or equal to unity\, and unstable when this thres
hold number is greater than 1. In the latter case\, the existence of at le
ast one endemic equilibrium (EE) (for the second model) and of a unique EE
(for the first model)\, which are locally asymptotically stable (LAS) is
shown\, together with the fact that the unique EE is GAS in the absence of
shedding and manipulation of deceased human individuals before burial. At
the endemic level\, it is shown that the number of infectious individuals
is much smaller than that obtained in the absence of any intervention. \n
\nIn a final step\, we construct nonstandard finite difference schemes tha
t are dynamically consistent with respect to the above features of the con
tinuous models.\n\nhttps://conferences.maths.unsw.edu.au/event/2/contribut
ions/122/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/122/
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SUMMARY:Dengue dynamics in Southern Mexico: an approximation to its popula
tion dynamics and the role of population movement
DTSTART;VALUE=DATE-TIME:20180709T063000Z
DTEND;VALUE=DATE-TIME:20180709T070000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-194@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Jorge Velasco-Hernandez (UNAM)\nUsing a data base o
n Dengue incidence available for four different states of the country we d
evelop mathematical models that describe the recurrent dynamics of cases a
t different geographical/regional levels. We present preliminary results.\
n\nhttps://conferences.maths.unsw.edu.au/event/2/contributions/194/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/194/
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SUMMARY:Signatures of within-host dynamics of dengue at a population level
DTSTART;VALUE=DATE-TIME:20180709T003000Z
DTEND;VALUE=DATE-TIME:20180709T010000Z
DTSTAMP;VALUE=DATE-TIME:20200813T134043Z
UID:indico-contribution-49-67@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Lauren Childs (Virginia Tech)\nVector-borne diseases
cause worldwide concern with hundreds of millions of new cases and over a
million deaths reported annually. Mathematical models are a key tool in t
he study of the spread of diseases such as malaria and dengue. In particul
ar\, transmission models have been successful at determining the most prom
ising intervention strategies\, despite the fact that many of these models
assume all individuals experience identical infections. Within-host dynam
ics of infections\, however\, vary widely among individuals. In the case o
f dengue\, within-host dynamics differ between primary and secondary infec
tions\, where secondary infections with a different virus serotype typical
ly last longer\, produce higher viral loads\, and induce more severe disea
se. Here\, we build upon models of variable within-host dengue virus dynam
ics resulting in mild dengue fever and severe dengue hemorrhagic fever by
coupling them to a population-level model. The resulting multiscale model
examines the dynamics of between-host infections in the presence of two ci
rculating virus strains that involves feedback from the within-host and be
tween-hosts scales. We analytically determine a threshold under which infe
ctions persist in the population.\n\nhttps://conferences.maths.unsw.edu.au
/event/2/contributions/67/
LOCATION:University of Sydney New Law School/--101
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/67/
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