Controlling an Influenza Outbreak in Deterministic and Stochastic Models with the Emergence and Evolution of Drug Resistance

In this paper first a system of ordinary differential equations is formulated for an extended SIR influenza model. In our model, the emergence of drug resistance and the evolution of resistant strains are assumed. As a result, the coexistence of sensitive and resistant strains leads to the occurrence of consecutive epidemic waves during the disease infection. We employ two main control strategies: prophylaxis and antiviral treatment to study their influences in eradicating or mitigating the outbreak. Then we develop a deterministic model to a SDE form for taking into consideration the stochasticity of drug resistance spread. The basic reproduction numbers and the control reproduction numbers are calculated for the sensitive and resistant strains. Also we discuss the numerical results obtained for the final size of the epidemic from both, the deterministic and stochastic models.