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NottinghamPhageN3AGPIIVIODE.m
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NottinghamPhageN3AGPIIVIODE.m
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function dy = NottinghamPhageN3AGPIIVIODE(t, y, sP)
% ODEs for a prey and two predators system
%
% Equations represent a batch system with an abiotic resource, prey species
% demonstrating monod kinetics, some of which show resistance vs predation,
% others which develop or lose persistance to predation and two predators
% one exhibiting a Holling type I functional response, the other a Holling
% type II response and mortality. Each predator has a seperate
% bdelloplast / infected cell stage. Development of persistence is %
% proportional to dead prey killed by bdellovibrio or phage.
% Persisters grow into sensitives
% Mode 17
%
% function dy = NottinghamPhageN3AGPIIVIODE(t, y, sP)
%
% dy - the rate equations
%
% t - time series
% y - initial species values
% sP - simulation parameters
% Version Author Date Affiliation
% 1.00 J K Summers 12/12/17 Kreft Lab - School of Biosciences -
% University of Birmingham
% 1.01 J K Summers 08/10/18 Ongoing developement as well as initial
% phage resistance
%
% Initial numbers of individuals in species being modeled
sub = y(1); % substrate value in fg/ml
senPrey = y(2); % Sensitive cells in cells / ml
bdPersistPrey = y(3); % Bdellovibrio persistor cells in cells / ml
phageResPrey = y(4); % phage resistant cells in cells / ml
bd = y(5); % Bdellovibrio cells in cells / ml
bdplast = y(6); % Bdelloplasts in cells / ml
phage = y(7); % Phage virions in virions / ml
infCell = y(8); % Infected cells in cells / ml
deadPrey = y(9); % Dead prey cells in cells / ml
% Rates for processes
dSub = -(senPrey + bdPersistPrey + phageResPrey) * sP.muMaxPrey * sub / ...
((sP.Ksn + sub) * sP.yieldNPerS) + ...
sP.yieldSPerV * sP.kV * infCell + ...
sP.yieldSPerP * sP.kP * bdplast;
% Bdellovibrio persistence is phenotypic so persistor bacteria divide to
% give sensitive bacteria
dSenPrey = (senPrey + bdPersistPrey) * sP.muMaxPrey * sub / ...
(sP.Ksn + sub) - ...
bd * sP.muMaxPred1 * senPrey / ...
((sP.Knp + senPrey + bdPersistPrey + phageResPrey) * ...
sP.yieldBPerN) - ...
phage * sP.muMaxPred2 * senPrey / sP.yieldIPerN - ...
senPrey * sP.rateDevPersist * deadPrey - ...
senPrey * sP.rateDevResistance;
dBdPersistPrey = - phage * sP.muMaxPred2 * bdPersistPrey ...
/ sP.yieldIPerN + ...
senPrey * sP.rateDevPersist * deadPrey;
dPhageResPrey = phageResPrey * sP.muMaxPrey * sub / (sP.Ksn + sub) - ...
bd * sP.muMaxPred1 * phageResPrey / ...
((sP.Knp + senPrey + bdPersistPrey + phageResPrey) * sP.yieldBPerN) + ...
senPrey * sP.rateDevResistance;
dPred1 = sP.kP * bdplast - ...
bd * sP.muMaxPred1 * (senPrey + phageResPrey) / ...
((sP.Knp + (senPrey + bdPersistPrey + phageResPrey)) * ...
sP.yieldBPerP) - ...
sP.mortality * bd;
dBdelloplast1 = bd * sP.muMaxPred1 * (senPrey + phageResPrey) / ...
(sP.Knp + (senPrey + bdPersistPrey + phageResPrey)) - ...
sP.kP * bdplast / sP.yieldPPerB;
dPred2 = sP.kV * infCell - ...
phage * sP.muMaxPred2 * (senPrey + bdPersistPrey) / sP.yieldIPerV;
dBdelloplast2 = phage * sP.muMaxPred2 * (senPrey + bdPersistPrey) - ...
sP.kV * infCell / sP.yieldVPerI;
dDeadPrey = sP.kP * bdplast / sP.yieldPPerB + sP.kV * infCell / sP.yieldPPerB;
%write results
dy = [dSub; dSenPrey; dBdPersistPrey; dPhageResPrey; dPred1; ...
dBdelloplast1; dPred2; dBdelloplast2; dDeadPrey];
end