Researchable or impossible choice of topic:
Insights from summer schools
by
J.Y.T. Mugisha
Biomathematics Modelling Group
Makerere University
Lecture presented at DIMACS Advanced Study Institute,
Makerere University,
20 – 31 July, 2009
Thursday, 30 June 2016
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Introduction
•
The choice of topic to research on during summer school is supposed
to be stimulated from the rather few, very fast presentation from
guest lecturers
•
Guest lecturers often assume an audience that is both biologically
and mathematically stable
•
there is little time for a summer school student to read and internalise
the lecture
•
Then, time comes and the students are put in groups; of varying
background
•
by the end of the day there is a problem to formulate. The question
is, when does the topic look researchable or impossible?
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CLUES from Other Summer Schools
• In the following slides, I give a few lessons from other
summer schools on the choice of subject to research on
and highlight the interesting patterns of topic choice
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Nature of models
•
Many epidemics take the usual dynamics of being SI, SIS, SIR, SIRS,
SIRZ, SEI,SEIS, SEIR, SEIRS, with others getting new names after
identifying their development pattern such as SVI
•
Then the nature of modelling involved depends on the individual
mathematician expertise and the characteristics of the epidemic:
Deterministic ODES, Stochastic Models, Delay ODES, Discrete Models
such as in patched space, PDEs as in most vaccination models
(Measles, Pertussis, Malaria, HIV/AIDS) and structured models (Age,
size, shape)
•
Also the nature of model analysis depends on the orientation of one's
mathematical skills: You will find a pure mathematician tackle the
model analysis from pure mathematics angle, a dynamical systems
person goes straight to finding strange attractors and whether there
will be chaos in the system, an applied mathematician formulating
and analyzing towards that direction and an algebraist must bring in
algebraic approach.
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But looking for what?
• In all, there are basic fundamentals that we need the model to
bring out on an epidemic
• what is the epidemic curve (describing the intensity of the
outbreak)?
• what is the death impact?
• economic impact?
• what is the level of disease incidence (no. of new occurences)
and prevalence
• what is the basic reproductive number
• any equilibrium (steady) states and what is the nature and
conditions (for) of their stability?
• Through these questions and of course, others coming out of
the "system study" (literature and on-spot data about the
disease) results regarding your model start to take shape.
• BUT are these known concepts before a student embarks on
the battle of topic choice
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Model
•
•
•
•
•
•
The model you would like to formulate is to eradicate the disease
completely (disease-free population),
or to have it to a contained situation (stable endemic state)
or to have a control measure to hold its devastation in cases of reemerging infections (vaccination).
In cases of endemic situation, you want to suggest best treatment
regimes and protocols to enable effective patient administration, costeffective drug administration and less drug resistance.
If it is a re-emerging disease, there would be literature on the way it
attacks, forms and patterns of outbreak and how existing models
were formulated and what they are targeting.
This gives you a clue on designing a new model to address the
failures of the previous one. This also may call for new parameter
definition and estimation. Therefore, the borrowing from the existing
models of the same diseases would help one not to waste much
research time identifying a problem, formulating, solving, validating
and improving the model.
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In case of emerging epidemics, they are in may cases new outbreaks.
These come as a surprise and every person (health worker, technocrat and
beaurocrat) in the process of scampering around suggests a possible control
measure.
To a mathematician, study the situation (do not take too long studying the
situation however!).
Find out the the epidemiological and demographic patterns of the outbreak,
then may be you will be able to characterize the epidemic as an SI, SIS, SIR,
SIRS, SEIR and build from there. Of course not all will be based on the
mentioned types of models. You will find yourself baptizing yours after a
while of formulation efforts like MSEIR and MSEIRS in Hethcote (2000).
Maybe the characteristics of a new and outbreak are similar to the one that is
existing, or that was eradicated. This is where literature comes in to play an
important role to address such a situation in building a model.
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What is it that is modelled
•Below, I present a couple of examples of
models developed from simple to complex,
giving a reflection that would answer questions
as to: Do mathematical models exist for any
disease or epidemic?
•This exposition should bring excitement to the
reader to dig even far back in literature, the
genesis of use of mathematical modelling in
epidemiology.
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Human-Mosquito Interaction model for mosquito
control
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Mosquito model
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What do the terms mean
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Are assumptions to this model realistic and where
do you get them from?
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…
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Tuberculosis Model with slow and fast progression
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Improved dynamics?
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Simple model for dynamics of streptococci infections
(MTBI 1999)
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Herpes Zoster
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And Foot-and Mouth Disease Model base on county
metapopulation
• FMD spreads very fast in a given region once not checked.
• An affected region is made up of counties.
• In the county are farms or call them patches assumed to
homogeneous mixing of animals.
• But the habitats or patches are heterogeneously distributed in
activity and characteristics.
• FMD is checked by Vaccination (mass or ring), Isolation
(Quarantine) and/or mass destruction of the affected animals.
• Let us take a ring vaccination strategy (effective in reducing
high risk, movement).
• What is the effective ring size to adopt to balance two goals:
prompt vaccination and vaccinating over as large an area as
possible without animal movement.
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Simple Model for FMD
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What does this model want to do?
• We need to now carry out a vigorous protection after
detection of an infected farm. We apply a reactive
response approach with ring vaccination.
• reactive in that control measures are implemented only
after an outbreak has been reported
• responsive in that we target vaccination according to
which farms have been diagnosed with FMD
• Ring vaccination means vaccinating in a ring with
certain radius around the diseased counties.
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Anything achieved?
• The idea behind ring vaccination is that farms that have
close contact with an infected one are at higher risk of
becoming infected and hence must be protected
• To have a bigger coverage of the counties this model can
be refined to incorporate spatial dynamics.
In such a way, we would address the transmission for
inter-county and intra-county .[Further reading see Keeling
\& Woolhouse, 2003, Chowell, G, et al., 2005; Diaz, E. et
al 2006)
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The Crude HIV/AIDS Model: Where
are we building from? (1986 model)
• Assume recruitment by births
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Trends in HIVAIDS Modelling
• From this model, one was able to changes
in parameters when treatment is
introduced, when one takes good diet,
when one used a condom, when one
practices zero-grazing (being faithful to
one sexual partner) etc. Since then,
excellent models have been built on this
and mathematical modellers are adding on
new improvements with advances other
efforts to contain the epidemic.
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Discussion…
Many other models available and improvements needed
•
Cholera
•
Sleeping Sickness (Trypanosomiasis)
•
Bilharzia (Schistosomiasis) and helminths through snails in lakes (Anderson and May (1991))
•
River Blindness (Onchocerciasis)
•
Tumor and cancer growth and therapy
•
Meningitis
•
Chagas (Busenberg and Vargas), Pertussis (Hethcote)
•
Polio, Measles, and their vaccination strategies
•
Many of the STDs (Gonorrhea, syphilis, Candida etc)
•
Influenza
•
Diabetes mellitus (Mahan
•
West Nile Virus, baboonic fever, rift valley virus
•
new emerging infections such as SARS and Bird flu
•
Zoonotic diseases: Tick-borne diseases as East Coast fever, Nagana
•
Plant diseases: Coffee and banana wilt, cassava mosaic
•
dispersal models
•
and modeling pathogenesis and treatment
•
Criss-cross Models
•
Mathematical Epidemiology ideas to social models
•
Within Host models and co-infection models
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END..
THANK YOU
and special thanks to DIMACS
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