Superinfection

The queuing models SquIP and SquIPz output MoI distributions in cohorts as they age.

The MoI distributions generated by realistic queuing models are reasonably well approximated by a negative binomial distribution.

We make a strong claim that the family of enhanced compartmental models SIPm, which is much simpler than the queuing models, is sufficiently accurate to use in place of the models SquIP and SquIPz. Specifically, we claim:

For every queuing model, we can develop a model SIPm that computes the dynamics of the first two moments of the distribution of the MoI, $m_1$ and $m_2.$ Specifically, we claim that the distribution of the MoI among infected individuals is well-represented by a zero-truncated negative binomial distribution: $$\mbox{dnbinom}(\mbox{mu}=m_1, \mbox{size}=\phi)$$ where $$\phi = \frac{m_1^2}{m_2 - m_1^2 - m_1}$$

Further, we claim that the dynamics of the two models are reasonably close. This rests on the assumption that $$r I_1 \approx F_r(m_1, m_2)$$

Workflows

Here, we define some workflows to explore those claims:

1. Specify a model:

   • $h(a)$ has a mean, a seasonal signal, and an age component

   • The Tweedie distribution has a specific form

   • Drug taking rates vary

2. Solve

   • Solve the queuing model

   • Solve the approximating model

3. Compare

   • Use the coefficient of variation to summarize