Assumptions and notation:

There are 2 antibiotics A and B and 4 strains of bacteria: rr is nonresistant,
Rr resistant on A, rR resistant on B and RR resistant on both A and B.
The population is divided into 5 groups X, Yrr, YrR, YRr, YRR, 
meaning healthy (susceptible), and infected with rr, rR, Rr, RR. 
a and b denotes the "level of usage" of antibiotics A and B. If a increases,
then the fraction people in Yrr and YrR which get cured icreases. However,
the fraction of people, who develop the resistant strain (move from
Yrr to YRr and from YrR to YRR) also increases. Similarly for b.

Flows between the groups.

from X to Yrr = srr X Yrr . srr is a parameter which indicates what fraction
of interactions between X and Yrr results in infection. 

Similarly from X to YrR, YRr, YRR.

from YrR to X = crR YrR + drR (1-crR) YrR . The first term represents people
who get cured. The coefficient crR depends on the level of usage of A, 
for example crR = 1 - 0.5^a . The second term represents people who are not 
cured and die. They are replaced by healthy ones to maintain the population size
(moved to X to balance the flow).
 
Similarly from YRr to X and from Yrr to Yrr to X. In the last case 
crr=1-0.5^{(a+b)/2}.

from YrR to YRR =  mrR (1 - crR) (1-drR) YrR . These are the people infected
with rR strain who don't get cured, don't die and develop the strain resistant
to both antibiotics, mrR = 1 - 0.5^{krR a}. krR is a constant which measures
the influence of the level of usage of A to the probability of developing the 
resistant strain.

Similarly from YRr to YRR.

>From Yrr to YRr = a/(a+b) mrrA (1-crr) (1-drr) Yrr . mrrA represents the 
probability that a patient who doesn't get cured doesn't die and is treated 
with A (the factor a/(a+b) - patient treated with A rather than B) developes the
strain resistant on A, mrrA= 1 - 0.5^{krrA a}.

Similarly from Yrr to YrR.

Finally, from YRR to X = mRR YRR, mRR represents mortality in YRR. People
who die are replaced by susceptible ones to maintain the population size and
balance the flows. Nobody gets cured in this group (unless we take garlic 
into account).

The flows may be realized in discrete or continuous time. Given the
parameters we want to find a and b, may be varying in time and depending on the
groups sizes, which minimize the number of people who die in the long term.