How does movement couple local epidemic conditions?
Each patch can differ in disease transmission, recovery, or population composition. Movement carries those differences across the network.
Research
How movement changes
what persists.
I study infectious-disease models in connected populations: how movement between places changes equilibria, disease persistence, and the long-run behavior of an epidemic system.
Mathematical epidemiology is the intellectual center of my work. Scientific machine learning extends that foundation; it does not replace it.
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Research overview
A simple question with a spatial answer.
If two communities have different disease conditions, what changes when people can move between them?
The answer depends on more than a single transmission rate. Movement connects local dynamics, redistributes populations, and can alter which steady states exist or remain stable.02
SIS models, simply
Infected, recovered—for now—and susceptible again.
An SIS model is appropriate when recovery does not create lasting immunity. People move from susceptible to infected and, after recovery, back to susceptible. The model is deliberately spare: that makes the mechanisms behind persistence easier to isolate.
SSusceptible
infection →Can acquire the infection.
IInfected
recovery ↺Can transmit before recovery.
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Movement & heterogeneity
Connected places are not interchangeable.
Represent place explicitly.
I use network and patch models that track susceptible and infected populations in multiple locations, with movement terms linking their dynamics.
A local condition can become a system-wide one.
A patch should not be interpreted in isolation once populations circulate. The connected system can admit behavior that no single patch predicts on its own.
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Analytical & numerical approach
Proof where structure allows it. Computation where behavior needs to be seen.
Equilibrium analysis
Identify disease-free and endemic steady states and the conditions under which they exist.
Stability
Study whether small perturbations decay or change the long-run behavior of the system.
Bifurcation questions
Track how qualitative behavior can change as movement or epidemiological parameters vary.
Numerical investigation
Use numerical simulations to examine cases that sharpen or extend the analysis.
Featured contribution
2026
Complex structure in the endemic equilibrium set of an SIS epidemic patch model with the mass-action infection mechanism
Coauthored with Rachidi B. Salako and published in SIAM Journal on Applied Mathematics, 86(2), 644–674. The article develops the endemic-equilibrium side of the mathematical epidemiology program described here.
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Dissertation trajectory
A research direction still in motion.
Doctoral research ongoingDo not infer results beyond published work
Established center
SIS network and patch models, population movement, spatial heterogeneity, endemic equilibria, persistence, stability, and bifurcation questions.
Current trajectory
Continue developing the analytical and numerical understanding of movement-driven behavior without treating ongoing dissertation questions as completed results.
Computational extension
Translate known differential-equation structure into scientific-machine-learning objectives for controlled parameter-recovery experiments.
Scientific-machine-learning extension
Equations become part of the learning signal.
In a disease-informed neural network, the differential equations are not merely used to generate data. Their residuals enter the training loss, giving the model a structural constraint alongside its observations.
See the synthetic-data experimentMathematical foundations
The work began before epidemiology.
Training in differential equations, functional analysis, and optimization shapes how I approach existence, stability, approximation, and constrained learning problems.
Follow the mathematical path