# CONCLUSION

We can easily understand the equilibrium reached for the chronic model:

dI = alpha_(i) k_(in) varphi S
Where alpha_(i) = lambda_(i) - delta or delta is neglicted,
so dI >= 0
Or I > 0 as there is some infection at the beginning.
dI = 0 only if:
• alpha_(i) = lamnda_(i) = 0, if S + I = Nstar
• k_(in) varphi S = 0 ⇒ S = 0 or varphi = 0
We conclude that S = 0 and I = Nstar or varphi = 0
If varphi = 0
As varphi = 0 as initial value, dvarphi < 0 in order to reach varphi = 0.
⇔ k_(out) I - k_(in) varphi S - delta_(varphi) varphi = 0
⇔ varphi < frac(k_(out) I)(k_(in) S + delta_(phi)) > 0

So I is strictly growing until S=0 and I=Nstar
At the equilibrium:
dvarphi = 0 ⇔ varphi= frac(k_(out) Nstar)(k_(in) S delta_(varphi))
Or S = 0
varphi = frac(k_(out) Nstar)(delta_(phi))

It is the same whatever the MOI (multiplicity of infection) is and whatever the proportion of initial bacteria depending on the load capacity is.

It is more difficult to do such demonstration for the lytic equilibrium as the behaviour is a little more complicated (see Drylab : results). There are two types of equilibrium stable or not, this is due to the latency time that is added. This value corresponds to the time after which a bacteria will die when infected by a lytic phage.

Our models are to be discussed on many points. First of all the bacteria death is neglected which is not representative, even more in the chronic model as it means the bacteria cannot die in this model, they reach the load capacity and it is over. Moreover, we work on an average number of phages per cell which is not really representative as each bacteria does not count in reality the same number of phages. It can depend on its localization for example between bacteria that are between cancer cells and bacteria that are in the tumor cells. Finally the form of the metabolic cost is not optimal and another more elaborated could be used in order to see and study more the impact of the phage infection on the bacteria metabolism, growth and death.