The transitions between model compartments for season
. In this model, S (t) is the number of fully susceptible individuals at the beginning of the current season; V
0 (t) is number of individuals who received vaccines for the current season; V
(t) is the number of individuals whose last vaccination was given i seasons ago; V
(t) is the number of previously vaccinated individuals who also received vaccination for the current season; r(t, α) is the number of individuals who were recovered from infection at time α (0 < α < m
1); R (t) is the total number of recovered individuals at time t; R
(t) is the number of previously recovered individuals who received vaccination for the current season; I (t) is the number of infections at time t during the current season; and γ is the rate of recovery from infection.