Figures & data
Figure 1. Solution P(t) to the periodic logistic differential Equationequation (1) with P(0)=1030 converges to a periodic solution P*(t) with period p=3 years and [Pcirc]=1516. Parameter functions b(t), d(t), and k(t) are defined in the text.
![Figure 1. Solution P(t) to the periodic logistic differential Equationequation (1) with P(0)=1030 converges to a periodic solution P*(t) with period p=3 years and [Pcirc]=1516. Parameter functions b(t), d(t), and k(t) are defined in the text.](/cms/asset/848f848f-d4f6-49d5-803c-bdc092f74a45/tjbd_a_330656_o_f0001g.gif)
Figure 2. Number of infectious individuals I(t) for the SIRS model Equation(6). For solutions graphed in (i) and (iii), we assume standard incidence, whereas in (ii) and (iv), we assume mass action incidence. The parameters b(t), d(t), k(t), γ (t), ρ(t), and β(t) are defined in the text, S(0)=1000, I(0)=30, and R(0)=0. (i) Standard incidence, βˆ=3.6 and ˆℛ0=0.90. (ii) Mass action incidence, βˆ=0.0024 and ˆℛ0=0.91. (iii) Standard incidence, βˆ=4.4 and ˆℛ0=1.10. (iv) Mass action incidence, βˆ=0.003 and ˆℛ0=1.14.
Figure 3. The basic reproduction number for the SIRS model with mass action incidence is graphed as a function of the amplitude k 1 of the density-dependent mortality k(t)=0.001+k 1 cos(2π t/3). All other parameter functions are defined in the text, where βˆ=0.0025 and P(0)=1500.
