Projects
Research Codes
SIHR Model Visualization
2025
An interactive visualization tool for analyzing SIHR-IPC (Susceptible-Infected-Hospitalized-Recovered with Individual Possion Clock) epidemiological models.
Mathematical Model
The SIHR-IPC model is described by the following system of ordinary differential equations:
\[\frac{ds}{dt} = -p_{SI}\beta si\]
\[\frac{di}{dt} = p_{SI}\beta si - \gamma(1-p_{II})i\]
\[\frac{dh}{dt} = p_{IH}\gamma i - p_{HR}\alpha h\]
\[\frac{dr}{dt} = p_{IR}\gamma i + p_{HR}\alpha h\]
where:
- \(s\): Susceptible proportion
- \(i\): Infected proportion
- \(h\): Hospitalized proportion
- \(r\): Recovered proportion
- \(\beta\): Transmission rate
- \(\gamma\): I outflow rate
- \(\alpha\): H outflow rate
- \(p_{SI}\): Probability of S→I transition
- \(p_{II}, p_{IH}, p_{IR}\): I outflow probabilities (sum = 1)
- \(p_{HR}, p_{HH}\): H outflow probabilities (sum = 1)
Key threshold parameters:
- \(\sigma = \frac{p_{SI}\beta s_0}{\gamma(1-p_{II})}\): Basic reproduction number
- \(\tilde{\sigma} = \frac{\gamma p_{IH} i_0}{\alpha p_{HR} h_0}\): Initial condition ratio
- \(\tilde{\tilde{\sigma}} = \frac{\gamma p_{IH} i_{peak}}{\alpha p_{HR} h(t_{pi})}\): Peak condition ratio
SIHRS Model Visualization
2025
An advanced interactive visualization tool for analyzing SIHRS (Susceptible-Infected-Hospitalized-Recovered with Death) epidemiological models with reinfection dynamics and mortality tracking.
Mathematical Model
The SIHRS model is described by the following system of ordinary differential equations:
\[\frac{ds}{dt} = -\beta p_{SI} si + p_{RS}\Lambda r\]
\[\frac{di}{dt} = \beta p_{SI} si - \gamma(1-p_{II})i\]
\[\frac{dh}{dt} = p_{IH}\gamma i - \alpha(1-p_{HH})h\]
\[\frac{dr}{dt} = p_{IR}\gamma i + p_{HR}\alpha h - p_{RS}\Lambda r\]
\[\frac{dd}{dt} = p_{ID}\gamma i + p_{HD}\alpha h\]
where:
- \(s\): Susceptible proportion
- \(i\): Infected proportion
- \(h\): Hospitalized proportion
- \(r\): Recovered proportion
- \(d\): Death proportion
- \(\beta\): Transmission rate
- \(\gamma\): I outflow rate
- \(\alpha\): H outflow rate
- \(\Lambda\): R outflow rate (reinfection)
- \(p_{SI}\): Probability of S→I transition
- \(p_{II}, p_{IH}, p_{IR}, p_{ID}\): I outflow probabilities (sum = 1)
- \(p_{HH}, p_{HR}, p_{HD}\): H outflow probabilities (sum = 1)
- \(p_{RR}, p_{RS}\): R outflow probabilities (sum = 1)
ND₁ Sequence Generator
2025
An interactive tool for exploring the dynamics of Dyck vectors and integer partitions through the ND₁ transformation map.