Deterministic and Stochastic Modeling of Pneumococcal Resistance to Penicillin

A stochastic compartmental model of the progression of pneumococcal resistance to penicillin G in a human community is built, through intra-individual selection and inter-individual transmission. It is structured by the resistance level of colonizing bacteria and driven by jump intensity functions. The Markov process associated with the model tends to the solution of a deterministic system when the size of the population tends to infinity. The behavior of the stochastic mean sample path is simulated for small population sizes and compared to the solution of the limit deterministic system. For populations over 5,000 individuals, the deterministic solution is a good approximation of the mean stochastic sample path. Both stochastic and deterministic predictions have proved useful to understand resistance selection mechanisms and to evaluate strategies for resistance prevention, such as a reduction in antibiotic consumption or vaccination.