Cellular Automata (CA) and Lattice Models represent a vital class of microscale epidemiological modeling frameworks, allowing disease spread to be examined at high spatial and individual resolution. These models discretize space into cells arranged on a lattice and time into sequential updates. Instead of relying on macroscopic averages found in classical Ordinary Differential Equation models, … Read more
Sophisticated spatial models are essential for understanding diseases transmitted between hosts and vectors, such as West Nile Virus. The spread of this virus across large geographic regions requires mathematical frameworks that couple infection dynamics with spatial movement. Reaction–diffusion models accomplish this by representing the spatial densities of hosts and vectors and by accounting for their … Read more
Partial Differential Equation (PDE) models are used in mathematical epidemiology to move beyond the simplifying assumption of homogeneous mixing, allowing for the representation of disease dynamics in continuous space (x) and time (t). Reaction–Diffusion systems describe both the biological progression of disease (reaction) and the spatial dispersal of hosts (diffusion). This framework is essential for … Read more
Agent-Based Models (ABMs), also known as micro-simulation models, are essential when population heterogeneity—differences in movement behavior, contact patterns, susceptibility, or adherence to interventions—plays a central role in disease spread. Unlike classical compartmental models that assume homogeneous mixing, ABMs simulate infection dynamics at the level of individual agents. 📐 Compartmental Structure and Flow Explanation ABMs consist … Read more
Partial Differential Equation (PDE) models, often expressed as Reaction–Diffusion systems, provide a mathematical framework for analyzing disease spread in continuous space and time. They extend traditional Ordinary Differential Equation (ODE) models by representing both the local spread of infection (reaction) and the geographic movement of hosts (diffusion). This approach is essential for understanding large-scale epidemic … Read more
Metapopulation (or Patch) Models are essential frameworks in mathematical epidemiology for incorporating discrete spatial heterogeneity into the analysis of infectious disease transmission. Rather than assuming homogeneous mixing across one large population, these models divide the geographic domain into distinct spatial units or patches (such as regions, cities, communities) and explicitly model how disease spreads within … Read more
Classic epidemic models often assume a closed population over short timescales where demographic factors are negligible. For analyzing long-term behavior or diseases that persist for years, the inclusion of Vital Dynamics—recruitment (birth) and natural death—is essential. These mechanisms allow the model to maintain a continuous influx of susceptible individuals, enabling endemic persistence even after the … Read more
Multi-group (or multi-patch) compartmental models are indispensable for accurately simulating infectious disease dynamics when the population structure is highly heterogeneous. By segmenting the total population into distinct interacting subgroups—such as age classes, regions, or behavioral cohorts—these models move beyond the homogeneous mixing assumption of classical SIR models to capture differential risks of infection and transmission … Read more
The assumption of exponentially distributed waiting times in classic compartmental models leads to the mathematically convenient, but often biologically restrictive, memoryless property. Age-of-Infection Models (also known as Time-Since-Infection, TSI models) address this by explicitly incorporating the time spent in an infected state (τ) as a determinant of contagiousness, infectivity profile, and probability of recovery. This … Read more
Age-structured compartmental models are essential tools in mathematical epidemiology for moving beyond the simplification of homogeneous mixing to capture realistic variations in disease transmission, contact patterns, susceptibility, and clinical outcomes across different demographic groups. By partitioning the population into discrete or continuous age classes, these models provide the high-resolution necessary for accurate policy evaluation, particularly … Read more