Special Issue “Mathematical Modeling of Viral Infections”
Abstract
How an infection will progress in the body is dependent on myriad factors: the rate of spread of the agent, the immune response, what treatment may be applied, .... Clinically following the progression of the disease is limited to snapshots at discrete time points (longitudinally in an individual or in an in vitro/animal model if that is available, but most often from cross-sectional data over cohorts of individuals), and in many cases the data obtained are from a body compartment that is not the site of replication of the disease.
Full text
i uses
Edi o ial
Special Issue “Ma hema ical Modeling o
Vi al In ec ions”
John M. Mu ay 1,2,*ID and Ruy M. Ribei o 3,4,*
1School o Ma hema ics and S a is ics, UNSW Aus alia, Sydney 2052, Aus alia
2Cance Resea ch Di ision, Cance Council NSW, Woolloomooloo NSW 2011, Aus alia
3Theo e ical Biology and Biophysics, Los Alamos Na ional Labo a o y, Los Alamos, NM 87545, USA
4Labo a o io de Bioma ema ica, Faculdade de Medicina da Uni e sidade de Lisboa,
1649-028 Lisboa, Po ugal
*Co espondence: j.mu [email protected] (J.M.M.); [email p o ec ed] (R.M.R.)
Recei ed: 25 May 2018; Accep ed: 28 May 2018; Published: 4 June 2018
How an in ec ion will p og ess in he body is dependen on my iad ac o s: he a e o sp ead o he
agen , he immune esponse, wha ea men may be applied, .... Clinically ollowing he p og ession
o he disease is limi ed o snapsho s a disc e e ime poin s (longi udinally in an indi idual o in an
in i o
/animal model i ha is a ailable, bu mos o en om c oss-sec ional da a o e coho s o
indi iduals), and in many cases he da a ob ained a e om a body compa men ha is no he si e o
eplica ion o he disease. We hen in e disease p og ession by pu ing hese disc e e da a oge he
based on ou biological knowledge o he sys ems in ol ed. Howe e , based on hese snapsho s,
i is no s aigh o wa d o wo k ou impo an disease p ope ies, such as he a e o p og ession,
pa hogenici y, and ea men and immune esponse e ec s. Ma hema ical modelling p o ides a
scien i ically sound, ep oducible me hod o desc ibe he unde lying dynamics ha p oduce hese
da a, as well as a means o in es iga e new scena ios, such as he e ec o a new d ug. I s impac
has been demons a ed on a numbe o diseases, o example, con ibu ing o a be e unde s anding
o he speed wi h which human immunode iciency i us (HIV) eplica es [
1
,
2
], he dynamics o
di e en d ug classes o HIV [
3
], he main mode o ac ion o in e e on in hepa i is C i us (HCV) [
4
],
he e ec s o di ec -ac ing an i i als in HCV [
5
], po en ial e ec s o he immune esponse [
6
], and many
o he s [7–11].
This issue on ma hema ical modelling o i al in ec ions co e s a numbe o i uses: HCV [
12
–
15
],
hepa i is B i us (HBV) [
16
,
17
], HIV [
18
], in luenza [
19
], and e en i uses ha a e used o comba
cance [
20
]. Mo eo e some o he modelling, al hough applied o speci ic diseases, has wide
applica ions as hey desc ibe in acellula p ocesses ha a e common o a numbe o in ec ions [
12
–
14
].
Bingham e al. p o ide a desc ip ion o he i al encapsida ion p ocess media ed by packaging
signalling (PS) mo i s, how his can esul in a measu e o i al i ness dependen on how well his
packaging occu s, and hen assess how a ge ing hese conse ed egions o he i al genome could
p oduce HCV he apies ha a e less suscep ible o i al escape han cu en di ec ac ing agen s [
14
].
The wo wo ks by Knodel and collabo a o s desc ibe in acellula dynamics o HCV p o eins and
i al RNA o e he endoplasmic e iculum (ER) and memb anous webs wi hin he cy oplasm [
12
,
13
],
which will ha e wide applica ion o o he in ec ions ha use simila pa hways o i al eplica ion,
assembly and expo (po en ially o he Fla i i idae such as Wes Nile Vi us, Dengue i us, and Zika
i us).
The con ibu ion o cellula p oli e a ion and i s subsequen ole in elimina ion o HBV a acu e
in ec ion is desc ibed by Goyal e al. [
16
]. Ganuso desc ibes he escape a e o HIV agains he CD8+
T cell esponse and how hese es ima es a e a ec ed by he ime be ween i al sequence sampling [
18
].
As on de elops a new HCV model and conside s i s implica ions o ea men [
15
]. The impac o
Vi uses 2018,10, 303; doi:10.3390/ 10060303 www.mdpi.com/jou nal/ i uses
Vi uses 2018,10, 303 2 o 3
an i i al he apy was in es iga ed by se e al g oups. Rod iguez e al. de e mined he p ocesses and
s a e o ch onic HCV in ec ion ha delinea ed he pa e ns o i al decay unde he apy [
17
]. Cao and
McCaw compa e he wo main ypes o in luenza models and desc ibe he bes ci cums ances o each
model’s use o p edic he esul s o an i i al he apy [19].
Oncoly ic i al he apy is a g owing a ea o esea ch. I uses i uses ha p e e en ially eplica e
in cance cells, ei he killing hem as a di ec esul o i al eplica ion, o h ough he induc ion o
immune esponses agains he cance . Fo hose eade s wan ing an in oduc ion o his impo an
and g owing ield, he e iew by San iago and collabo a o s p o ides an excellen co e age o he
unde lying biology o oncoly ic i al he apy as well as he app oaches o da e in ma hema ical
modelling in his a ea [20].
This issue also p o ides a good co e age o he di e en ma hema ical modelling app oaches ha
can be used. Mos o he models employed he e a e desc ibed by o dina y di e en ial equa ions (ODEs).
These ha e he ad an age o a mo e s aigh o wa d implemen a ion wi hin nume ical so wa e, as well
as equi ing ewe pa ame e s han agen -based models. Fo si ua ions when bo h space and ime
elemen s a e needed, such as in he wo k desc ibing i al p o ein mo emen wi hin HCV-in ec ed
hepa ocy es [
12
,
13
], pa ial di e en ial equa ions (PDEs) a e he na u al se ing ( o see how complex
hese dynamics can be and he geome y ha can be inco po a ed in o hese models, he eade is
di ec ed o he mo ies in he Supplemen a y Ma e ial o hese a icles). Finally, whe e mu a ions mus
be acked as is he case o he e olu ion o a i al quasi-species [
14
], a s ochas ic sys em o equa ions
is necessa y.
Finally, we no e he in e disciplina y aspec o hese wo ks, wi h au ho ships co e ing hospi als,
depa men s o medicine, biology, immunology, and oncology, high-pe o mance compu ing g oups,
as well as ma hema ics depa men s. These a e complex sys ems whe e he dynamics a e no easy
o unde s and and consequen ly equi e a ma hema ical desc ip ion. Bu ma hema ics is only one
aspec o success ully analysing he cou se o a disease. Any meaning ul con ibu ion equi es an equal
pa ne ship wi h ou biomedical collabo a o s. This Special Issue e lec s his impo an pa ne ship.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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