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Mathematical modeling

Network-Based SEIRV Epidemic Modeling

An age-structured network model of measles, combining community contact patterns, stochastic dynamics, vaccination, and displacement mechanisms.

Year
2026
Status
Ongoing
Topics
Epidemic models · Networks · Simulation

The project in brief

How do age structure, uneven vaccination, and contact between communities shape simulated measles dynamics?

How does an epidemic change when contacts, immunity, and displacement are distributed unevenly across a population? This project represents urban, rural, nomadic, and displaced communities as an age-structured network. Its central object is the force of infection: a map from the network's current state to each community's exposure.

The simulator is implemented; current work studies its dynamics and sensitivity. The equations and results below describe model mechanisms and numerical diagnostics, not a forecast calibrated to observed outbreaks.

Disease progression S → E → I → R, vaccination S → V, and community contact

A simplified SEIRV compartment sketch. The implementation also includes two maternal-immunity stages and an infant-vaccination state; this diagram is not the full transition model or a simulated trajectory.

Model

From a contact network to infection pressure

Community ii and age group aa receive exposure from infectious prevalence pp in source community jj and age group bb. CC is the recipient's age-contact matrix, ww is its community-contact composition, and β\beta is its time-dependent transmission parameter. Set p=0p=0 when N=0N=0. This is the ordinary urban/rural/nomadic channel (G0\mathcal G_0); displaced-population channels are separate. The method chapter defines the weights and compartment dynamics.

λia(0)(t)=βi(t)∑b=1mCab(i)(t)∑j∈G0wij(t) pjb(t),pjb=IjbNjb\lambda^{(0)}_{ia}(t) =\beta_i(t)\sum_{b=1}^{m}C^{(i)}_{ab}(t) \sum_{j\in\mathcal G_0}w_{ij}(t)\,p_{jb}(t), \qquad p_{jb}=\frac{I_{jb}}{N_{jb}}

Active model implementation: force-of-infection assembly and contact composition.

Question
How do age structure, immunity, and contacts between communities change recurrence and the distribution of simulated infection burden?
Method
Eight compartments per age/community pair, network-weighted infection pressure, competing-risk stochastic updates, and separate displacement mechanisms.
Progress
Initialization diagnostics and a 270-run displacement sweep identify which assumptions change recurrence and where infectious person-days accumulate.

Explore the project

01 / Problem

One population, several interacting scales

The mathematical question is how local disease transitions compose with age-dependent contact and a network of communities.

Read chapter 02 / Method

Compartment dynamics coupled through infection pressure

The construction has three layers: local reaction hazards, a contact-composition operator, and stochastic or deterministic time stepping.

Read chapter 03 / Progress & next steps

What changes the simulated dynamics?

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

Read chapter
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My contribution

  • Developing the networked mathematical model.
  • Building a modular simulation and reproducible experiment workflow.
  • Studying sensitivity to mobility and intervention assumptions.

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