9 problems

Consider the full system represented by the full model and the reduced system represented by the reduced model. The two systems have numerically similar long-term dynamics, with tr…

Let $\tau$ denote the cross-immunity parameter, with $0 \leq \epsilon \leq 1$, where $\tau=0$ represents no cross-immunity and $\tau=1$ represents full cross-immunity. Assume the c…

In the metapopulation framework, let $K$ be a next-generation matrix with non-negative entries, let \boldsymbol{[?]?

Agreement conjecture. The renewal equation agrees with the integral equation for incidence, namely

Consider the stochastic discrete-time SIR model with population size $N$, reproductive number $R_0$, and infection growth rate … When $\alpha<1$ (equivalently, $R_0<1$), the mean t…

Consider the deterministic discrete-time SIR model with reproductive number $R_0$ and its endemic equilibrium. The model is based on individual-based update rules with an exponenti…

Let $\tilde\mu,\tilde\beta,\tilde\gamma$ be positive or nonnegative continuous-time rate parameters, let $\Delta t>0$, and define the discrete-time parameters by … Let $R_0$ be the…

Let $\beta,\mu,\gamma$ be the SIS model parameters, let $N$ be the population size, and set … When $\alpha<1$, the quasi-stationary distribution describes the long-term transient b…

Consider the HIV/AIDS prevention model with AIDS-induced death rate $d>0$, and let the endemic equilibrium be denoted by $\Sigma_+$. Global asymptotic stability conjecture. The end…