Impact of emerging antiviral drug resistance on influenza containment and spread in a multi-drug strategy: Appendix S1

We provide details of the models used in the main text, explain some of the results in greater detail, perform a sensitivity analysis for each model and explore a number of alternate scenarios to demonstrate the general nature of the results presented in the main text. S1 Details of the model The models used in this paper are extensions to the contact model described in detail in McCaw and McVernon (2007). Here we detail how asymptomatic infections and development of antiviral resistance is accounted for within the single-drug model. We also provide R0 calculations for the single-drug model. The multi-drug model equations are presented for reference, while details of their construction are left to Appendix A. S1.1 The single-drug model We have states I p with y ∈ {w, r} representing symptomatic infections for those taking prophylaxis (p) and infected with the wild-type (y = w) or resistant-type (y = r) strain. States Ap represent equivalent asymptomatic infections. We also have the state I np,t representing symptomatic infections with the wild-type strain for those not taking prophylaxis (np), but being provided with antiviral drugs as treatment (t). For symptomatic infections with the wild-type strain that are not provided with antiviral drugs at all, we have the state I np,nt. Symptomatic infections with the resistant-type strain may or may not be provided with treatment but it has no effect so we require just one state I np. Asymptomatic infections are not able to be identified and provided with antiviral drugs and so we only require two states Anp with y ∈ {w, r}. The force of infection arises from each of these nine infectious classes: λp = βei ( I p + χA w p ) (S1) λnp,nt = β ( I np,nt + χA w np ) (S2) λnp,t = βetI w np,t (S3) λ = βφ ( I p + I r np + χ ( Ap + A r np )) , (S4) where φ is the relative transmissibility of the resistant strain relative to uncontrolled wild-type and χ is the relative transmissibility of asymptomatic infections. Other parameters are defined as in McCaw and McVernon (2007). Infections arising from these nine states cause susceptible individuals (S) to become exposed (E x with x ∈ {p, np} and y ∈ {w, r}). Exposed individuals will become infectious after a latent period of mean duration 1/ω days. New infections (I andA states) have contacts (C x states) which may or may not be exposed. The mean infectious period is 1/γ days. A susceptible, upon exposure, can proceed down a number of paths, dependent upon the characteristics of the infectee (wild-type, resistant-type) and whether or not they are provided with post-exposure prophylaxis. A proportion of exposures, α, are symptomatic. Our model allows for this proportion to depend upon the nature of the strain (w or r) and the provision of prophylaxis (p or np). Resistance development (“seeding”) is captured by two parameters. A proportion, ρt, of those exposed to wild-type virus and treated (α npψE w np) convert to become symptomatic resistant-strain