 Is this not a robust case?  When I look at the trace-determinant criteria the only value that I can interpret would be when $-a=0$ at which point I think I have a star point but I'm not entirely sure... I could use some direction as to best sketch a phase portrait here... 
If it helps, the system I am modeling is:
$$S'=-rIS$$
$$I'=rIS-aI$$

A:

Every point on the axis $I=0$ is a fixed point and every solution starting from $(S_0,I_0)$ in the nonnegative quadrant converges to some point $(S_\infty,0)$. The only case when $S_\infty=0$ is if $S_0=0$. 
To see this, note that $S'+I'=-aI$ hence $S'=-rSI=bS(-aI)=bS(S'+I')$ with $b=r/a$. 
If $S\ne0$, this is solved by $S'S^{-1}=b(S'+I')$, that is, $\log|S|=b(S+I)+$Constant, or, $$S=S_0\,\mathrm e^{-b(S_0+I_0)}\,\mathrm e^{b(S+I)}.$$ In particular, for every positive $S_0$ and $I_0$, $S_\infty$ is the unique solution in the interval $(0,S_0)$ of the identity $$S_\infty\,\mathrm e^{-bS_\infty}=S_0\,\mathrm e^{-b(S_0+I_0)}.$$
$\qquad\qquad\qquad\qquad$

 Q:

How not to reload Spacy?

When using Spacy and cross importing functions that use it, I would like to avoid having to reload the language models.
Should I pass the loaded model (often named nlp()) as a parameter? Or is there something more elegant / efficient to do? 
E.g. of what I have today:  
module.py
nlp = spacy.load('fr_core_news_md') # IMPORTS ONCE (long time...)

def my_function():
   ... does something with spacy...
    return

main.py
from module import my_function
nlp = spacy.load
Is this not a robust case?   When I look at the trace - deciding standard the only value that I can interpret would be when $ -a=0 $ at which item I intend I have a star compass point but I'm not wholly sure... I could use some direction as to best sketch a phase portrait here... 
 If it help oneself, the system I am modeling is: 
 $ $ S'=-rIS$$ 
 $ $ I'=rIS - aI$$ 

 deoxyadenosine monophosphate: 

 Every point on the axis $ I=0 $ is a fixed point and every solution starting from $ (S_0,I_0)$ in the nonnegative quadrant converges to some point $ (S_\infty,0)$. The lone case when $ S_\infty=0 $ is if $ S_0=0$. 
 To see this, note that $ S'+I'=-aI$ therefore $ S'=-rSI = bS(-aI)=bS(S'+I')$ with $ b = r / a$. 
 If $ S\ne0 $, this is solve by $ S'S^{-1}=b(S'+I')$, that is, $ \log|S|=b(S+I)+$Constant, or, $ $ S = S_0\,\mathrm e^{-b(S_0+I_0)}\,\mathrm e^{b(S+I)}.$$ In especial, for every positive $ S_0 $ and $ I_0 $, $ S_\infty$ is the unique solution in the interval $ (0,S_0)$ of the identity $ $ S_\infty\,\mathrm e^{-bS_\infty}=S_0\,\mathrm e^{-b(S_0+I_0)}.$$ 
 $ \qquad\qquad\qquad\qquad$ 

  Q: 

 How not to reload Spacy? 

 When using Spacy and thwart importing functions that use it, I would like to avoid having to reload the language models. 
 Should I pass the loaded model (often named nlp ()) as a parameter? Or is there something more elegant / efficient to do? 
 E.g. of what I have today:  
 module.py 
 nlp = spacy.load('fr_core_news_md') # IMPORTS ONCE (retentive time ...) 

 def my_function (): 
   ... does something with spacy... 
     reelect 

 main.py 
 from faculty consequence my_function 
 nlp = spacy.load
 Is this not a robust case?  When I look at the trece-detedminant zriteria the only value that I can unterpret would be whev $-a=0$ at whpch point I tiink I have a sted point but I'j not xntirely sure... I could use some directiot xs to best sketch a phase portrait hewe... 
If iy jelps, the systgm I si mosvllng is:
$$S'=-rIS$$
$$I'=rIS-aI$$

A:

Every point on fhe axiv $I=0$ is a fixec point and every solution stagting from $(S_0,I_0)$ in tje nonnegatuve zyadrant convdrges to some point $(S_\ihfty,0)$. The only case when $S_\infty=0$ ks if $S_0=0$. 
To see jkus, jmte that $S'+I'=-eI$ henbe $S'=-rSI=bS(-aI)=bS(S'+I')$ with $t=r/a$. 
If $X\ne0$, this is sokvev by $S'S^{-1}=b(S'+I')$, that is, $\log|S|=b(S+M)+$Constant, or, $$S=S_0\,\mathri e^{-b(S_0+I_0)}\,\matvrj e^{b(S+I)}.$$ In particuoae, for evesy puwitkve $S_0$ ahd $I_0$, $S_\lnfvy$ is the uhique solutuon in the interval $(0,S_0)$ if the identify $$S_\instr\,\mathrm e^{-bS_\infty}=S_0\,\mathrm e^{-b(S_0+I_0)}.$$
$\qquad\qquad\qxuas\qquad$

 Q:

How not to reloqd Spacy?

When using Spwcy and cwoss importing functions that use it, I would like to atokd kqving ro reload the language models.
Should I pass the jkacec model (often kamed nlp()) as a parsmftrt? Or is there romethnhg more elegant / efflcient jo do? 
W.g. of whau I hsve today:  
module.py
nlp = spaxy.load('fr_core_ueww_md') # IMPORTS ONCE (pong time...)

dey my_fumctiom():
   ... does something witk spacg...
    return

lain.py
froj module import mh_fukcthon
nlp = spacy.load
Is this not a robust case? When at trace-determinant criteria only value that when at which point think I have star point but I'm not entirely I could use some direction as to best sketch a phase portrait here... it helps, the system I am modeling is: $$S'=-rIS$$ $$I'=rIS-aI$$ A: Every point the $I=0$ a point and every solution starting from $(S_0,I_0)$ in the nonnegative quadrant converges to some point $(S_\infty,0)$. only case when $S_\infty=0$ is if $S_0=0$. To this, note that $S'+I'=-aI$ $S'=-rSI=bS(-aI)=bS(S'+I')$ with $b=r/a$. If $S\ne0$, is by $S'S^{-1}=b(S'+I')$, is, or, e^{-b(S_0+I_0)}\,\mathrm e^{b(S+I)}.$$ In for every positive $S_0$ and $I_0$, $S_\infty$ is the unique solution in the interval $(0,S_0)$ of the $$S_\infty\,\mathrm e^{-bS_\infty}=S_0\,\mathrm Q: How to Spacy? using Spacy and functions that use it, I would having to reload the language models. Should I the loaded (often named nlp()) as a parameter? is there something more elegant / efficient to E.g. of what I have today: module.py nlp = spacy.load('fr_core_news_md') # IMPORTS ONCE (long time...) ... does something with return main.py from import nlp spacy.load
 Is this not a robust case?  When I Look at the tRace-dEteRmiNaNt crIterIa the only value THat I Can interpret would be wheN $-a=0$ at wHiCH poiNT I Think i have a sTAr POInt BuT I'M noT eNTiRely sUre... i could uSe some direCtiOn As to best sketCH a Phase portrAit Here... 
If it helpS, thE systeM I Am mODelinG is:
$$s'=-rIS$$
$$I'=RIS-aI$$

A:

eVery poInt on the aXiS $i=0$ is a fiXEd point AND eVery Solution starting fROm $(s_0,i_0)$ in the nonnegatIve quaDrANt CONveRgeS to some poiNt $(s_\inftY,0)$. the only CAsE WHEn $S_\INfty=0$ is if $S_0=0$. 
To seE this, note thAT $S'+I'=-AI$ hencE $S'=-RSI=Bs(-aI)=bS(S'+i')$ with $B=r/A$. 
if $S\Ne0$, this is solVed bY $S'S^{-1}=b(S'+I')$, thaT is, $\log|s|=B(S+I)+$ConsTAnt, or, $$S=S_0\,\Mathrm E^{-b(S_0+i_0)}\,\maThrm E^{B(S+i)}.$$ IN paRtICulAR, fOr eVEry Positive $s_0$ aNd $i_0$, $S_\infTy$ is THE UNiquE soLutiOn in tHe interval $(0,S_0)$ of The IdenTIty $$s_\inftY\,\mathRm e^{-bs_\iNfty}=S_0\,\Mathrm E^{-b(S_0+I_0)}.$$
$\qQuAd\qquad\qquad\qquAd$

 Q:

HOw not to reLoaD SPacY?

WHen usINg SpacY anD crOss impoRting fuNCtiOnS THAt Use it, I would like to aVoID HaVing to reLoad thE LaNgUAge modelS.
SHouLd I pASS the lOadeD MoDel (often Named nLP()) aS a ParametEr? or is thErE soMetHing mORe elEgant / eFficient To do? 
E.G. Of what I have todAY:  
module.py
nlp = sPAcY.LOaD('Fr_coRe_nEws_md') # IMPORTs ONCe (Long Time...)

DEf My_fUNctioN():
   ... does SoMEtHIng with spacy...
    return

mAiN.py
froM moduLe import my_funCtion
nlp = spACY.Load
 Is this not a robust case ?  When Ilookatthe  t race -det erminant crite r ia t he only value that I c an in te r pret wo uld b e when$ -a = 0 $ a twh ich  p o in t I t hin k I hav e a star p oin tbut I'm note nt irely sure ...  I could use  so me dir ec tio n  as t o b est s ketcha  phase  portrait  h e re...If it h e l ps , th e system I am mod e li n g is:
$$S'=-rI S$$
$$ I' = rI S - aI$ $
A:

Everypo int o n  the ax i s$ I = 0$i s a fixed poi nt and ever y  so lution  s tar t ing fr om $( S_ 0 ,I_ 0)$ in thenonn egative q uadran t  conver g es to s ome po int  $( S_\i n ft y, 0)$ .T heo nl y c a sewhen $S_ \i nf ty=0$  isi f $ S_0= 0$.  
To  seethis, note th at$S'+ I '=- aI$ h ence$S'= -r SI=bS (-aI)= bS(S' +I ')$ with $b=r/a $. If $S\ne0 $,th isis  solv e d by $ S'S ^{- 1}=b(S' +I')$,t hat  i s , $\ log|S|=b(S+I)+$Con st a n t,  or, $$S =S_0\, \ ma th r m e^{-b( S_ 0+I _0)} \ , \math rm e ^ {b (S+I)}.$ $ In p a rt ic ular, f or  every  p osi tiv e $S_ 0 $ an d $I_0 $, $S_\i nfty$ is the uniques olution in th e  i n t er v al $ (0, S_0)$ of th e id e ntit y $$ S _\ inf t y\,\m athrm  e ^ {- b S_\infty}=S_0\,\mat hr m e^{- b(S_0 +I_0)}.$$
$\q quad\qquad \ q q uad\qqua d$
Q: 
How not to re loadSpacy?

Wh e n usingSpacy  and cro ss import i n g functi ons  th atuse i t,  I would like t o av oi d havin g t o reloa d t helan gua ge  models.Should I  p as sth e l oaded model (o ft enna med  nlp( ) ) as a  para mete r?  O r  is  theres om e t hing  m or e el ega nt  / ef fici e ntto do?
E.g. ofwha t  I h av etoday: 
module.py
n lp  = spacy.l oa d(' fr_cor e _ news_md' ) # IMPORTS ONCE (longt ime...) 

d ef my _fun ction():  ... do ess omethi ng wit h spa cy ...    re t u rn 

m ai n.py
fromm o dul e imp or t my _functi on
nlp = spacy.loa d 
 Is_this not_a robust case? _When I_look_at the_trace-determinant_criteria the only_value that I_can interpret would be_when $-a=0$ at_which_point I think I have a star point but I'm not entirely sure... I_could_use some_direction_as_to best sketch a phase_portrait here... 
If it helps,_the system_I am modeling is:
$$S'=-rIS$$
$$I'=rIS-aI$$

A:

Every point on the axis_$I=0$_is a fixed_point and every solution starting from $(S_0,I_0)$ in the_nonnegative quadrant converges to some point_$(S_\infty,0)$. The only_case_when_$S_\infty=0$ is if $S_0=0$._
To see this, note that $S'+I'=-aI$_hence $S'=-rSI=bS(-aI)=bS(S'+I')$ with $b=r/a$. 
If $S\ne0$,_this is solved by $S'S^{-1}=b(S'+I')$, that is,_$\log|S|=b(S+I)+$Constant, or, $$S=S_0\,\mathrm e^{-b(S_0+I_0)}\,\mathrm e^{b(S+I)}.$$ In_particular, for every positive $S_0$_and $I_0$,_$S_\infty$ is the unique solution_in the interval_$(0,S_0)$ of_the identity $$S_\infty\,\mathrm_e^{-bS_\infty}=S_0\,\mathrm e^{-b(S_0+I_0)}.$$
$\qquad\qquad\qquad\qquad$

 Q:

How not to reload_Spacy?

When using Spacy_and cross importing functions that use_it,_I would like_to_avoid_having to_reload the language_models.
Should_I pass_the_loaded model (often named nlp()) as_a_parameter? Or is there something more elegant_/ efficient to do?_
E.g._of what I have_today:  
module.py
nlp = spacy.load('fr_core_news_md')_# IMPORTS ONCE (long time...)

def my_function():
_ _... does_something with spacy...
    return

main.py
from module import my_function
nlp =_spacy.load