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
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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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