Dynamics of Single-City Influenza with Seasonal Forcing: From Regularity to Chaos

Figure 6

Environmental effects on basic reproductive ratio, 𝑅₀. (a) Seasonal change in virus inactivation rate, 𝑘_vir,env (Figure 1; (15), (18)), giving virus inactivation by temperature alone. 𝑇_air is mean daily air temperature (appropriate to southern Britain) (19); 𝑇_air0 is an assumed temperature threshold for virus inactivation, here equal to 13°C ((18), Table 1)); 𝑅_𝟎 is the seasonally modulated basic reproductive ratio (20), calculated assuming temperature is constant. (b) For different values of mean annual air temperature, 𝑇_air,mean (19), basic reproductive ratio 𝑅₀ (20) is seasonally modulated as in (a) via the seasonal modulation of 𝑘_vir,env, for a constant threshold temperature for virus inactivation of 𝑇_air0 = 13°C (18), giving for 𝑅₀ a maximum, minimum, annual mean, and amplitude (maximum-minimum). 𝑁_fdy denotes the number of forcing days per year (a “forcing day” is a day on which air temperature is sufficiently high as to increase virus mortality).

(a)

(b)