Abstract
In this work we present three different approaches that lead to models of ordinary and partialdifferential equations with delay for the in vitro dynamics of Salmonella enterica bacteria and
some of their attacking phages.
The experiments were designed, carried out and measured by a team of microbiologists and
our work as mathematicians consisted in proposing and validating these mathematical models
via comparisons versus experimental data.
Under these circumstances, the mathematical work to do was not initially determined, but
it was guided by the results of the comparisons that pointed out some required adjustments on
the models. For this purpose we developed computer programs that allowed us to run numerical
simulations of all the models we proposed.
In this way, each approach became more complicated than its predecessor, in mathematical
terms, at the same time it appeared more promising.
We conclude our first approach with an ordinary differential equations system with delay for
the interaction of m bacterial strains versus n distinct phages, based on the mass action law with
fixed adsorption constants and regarding a mutation rates coefficient matrix. We can include
resistant bacteria and divide bacterial strains into sub populations characterized by having the
same parameter values. One important issue is that we manage to treat super infections in an
appropriate way by allowing adsorptions on infected, dead and lysed bacteria.
In the second approach we structured a susceptible and a resistant bacterial populations by
the cell age and size, obtaining a system with three partial differential equations combined with
three single variable integro differential equations where a delay term is included in one of them.
The last approach deals with a physiologically structured system. We regard a susceptible
bacterial population with a structure by the number of receptors on the cell membrane, together
with the possibility of allowing a viral attach-detach mechanism as part of the absorption process.
We also consider one phage kind and a resistant bacteria population. This idea is presented in
a discrete and in a continuous fashion.
One thing we learned throughout this process is that there is still much work to be done, but
we have determined some paths to be followed that can produce good results in a near future
whenever the computing power continues raising as it does nowadays.
| Date of Award | 30 Sept 2011 |
|---|---|
| Original language | English |
| Supervisor | Angel Calsina Ballesta (Director) & Carles Perelló Valls (Director) |