Network SEIRV · Chapter 03

What changes the simulated dynamics?

Two diagnostic experiments examine recurrence and displacement. Both use zero vaccination; neither is observed-data calibration.

A model that can be interrogated

The implemented framework includes compartment dynamics, contact composition, displacement, repeatable scenarios, and mechanism-level checks. A deterministic screen found biennial-like recurrence for several transmission settings; the next question was whether stochastic runs preserve it.

Definition

Alternating annual peak contrast

$P_0$ and $P_1$ are median annual peak infectious prevalences in alternating years after the transient period. Set $\chi=0$ if both are zero. A value near one indicates a strong difference between alternating high- and low-peak years; it is one diagnostic, not a proof of an exact periodic orbit.

\chi=\frac{|P_0-P_1|}{\max(P_0,P_1)}

Alternating-peak statistic in the dynamics-classification implementation.

Deterministic reference on the production topology
Target mean unforced R₀	Median peak interval	Attractor period	Alternating peak contrast
9.75	24 months	2 years	0.862
10.25	24 months	2 years	0.890
11.25	24 months	2 years	0.927

Source: repository stochastic-sensitivity summary, deterministic reference. All three use the production topology and zero vaccination. R₀ values are targets from the single-node, unforced mapping used to select transmission parameters; they are not estimates fitted to case data or network-wide R₀ claims.

The same parameters do not imply the same recurrence

For the provisional R₀-target 11.25 setting, 30 stochastic runs began from the same simple 10% susceptible / 90% recovered profile with 20 urban infections introduced. Only the random seed varied. Most runs were classified annual-like; five faded out.

Thirty runs from one simple initial profile

Stochastic runs

Source: repository stochastic-sensitivity summary. Fixed simple initialization, 30 seeds, zero vaccination, closed dynamics. These are whole-run classifications; 13 runs still contained at least one biennial-like rolling 10-year window. They are not estimated real-world outbreak probabilities.

View plot data

Thirty runs from one simple initial profile: saved observations
Series	Full-run diagnostic classification	Number of runs
Stochastic runs	Annual-like	25
Stochastic runs	Fadeout	5
Stochastic runs	Biennial-like	0

Changing the starting state at the same transmission setting
Starting state	Runs	Full-run biennial-like	Any 10-year biennial-like window
Deterministic cycle: high-peak phase	15	4	14
Deterministic cycle: low-peak phase	15	5	11
Simple immunity profile + 20 infections	30	0	13

Source: repository stochastic-sensitivity summary, phase-sensitivity comparison for the provisional R₀-target 11.25 candidate. Rolling windows overlap; the last column counts runs containing at least one such window, not independent windows. Different initialization ensembles should not be pooled as a single probability estimate.

Where does additional simulated burden accumulate?

A separate sweep varied temporary-group size, affected rural fraction, and two rural-contact parameters: 54 settings × 5 seeds = 270 simulations. Each ran for 30 model years with four sampled shock events per year and zero vaccination. The table shows the reported grouped median burden, rounded to thousands of infectious person-days.

Rural infectious person-days remain near the same level across this grid.
The large change is concentrated in the main displaced population after transfer.
This supports a mechanism-specific interpretation of the simulator, not a general claim about real displacement or a causal effect estimated from observations.

Displacement sweep: rural versus main-IDP burden
Mean group size	Affected rural fraction	Rural IPD (thousands)	Main-IDP IPD (thousands)
20	0.1	353	192
20	0.5	354	299
100	0.1	352	320
100	0.5	355	882
500	0.1	354	966
500	0.5	355	3,860

Source: archived size-by-affected-fraction comparison and displacement sensitivity report. Groups aggregate the tested rural-mixing settings; they are not single matched trajectories or confidence intervals. Initial state and shock protocol differ from the simple-initialization experiment above. Five seeds per full scenario support diagnostics, not precise population-level estimates.

Open questions

The next stage is to challenge the mechanisms that produced these patterns, then repeat comparisons under vaccination.

How robust are recurrence classifications to initial immunity and seasonal forcing?
Does changing stopover duration or contact structure strengthen rural-side effects?
Do vaccination scenarios preserve the ordering of displacement sensitivities?
How stable are scenario summaries with more stochastic seeds?
Which parameters can eventually be identified from observations? Calibration and external validation remain separate future tasks.

Last updated September 26, 2026