Various tools for investigate the data in this data portal or models
🧭 Conceptual Overview In mathematical epidemiology, many classical models emphasize the acquisition of immunity following infection. In contrast, the Mean-field SIS model captures the dynamics of pathogens that do not induce long-lasting immunity. In this framework, individuals cycle repeatedly between being susceptible and being infectious. The population is assumed to be perfectly mixed, meaning each … Read more
🧭 Conceptual Overview In mathematical epidemiology, the Mass-action incidence SIR model represents one of the most fundamental and theoretically pure descriptions of infectious disease spread. Inspired by chemical reaction kinetics, this framework assumes that new infections occur through random “collisions” between susceptible and infectious individuals. The infection rate is therefore proportional to the product of … Read more
🧭 Conceptual Overview The Macdonald malaria model is a foundational mathematical framework for understanding transmission dynamics in vector-borne diseases. It formalizes the feedback loop between human hosts and mosquito vectors, capturing how infection is sustained through repeated biting events. This model underpins modern definitions of the basic reproduction number in vector-borne systems and provides direct … Read more
🧠 Why Lyapunov Control in Epidemiology? Classical SIR models describe how epidemics evolve, but they do not prescribe how to actively steer an epidemic toward a desired outcome. The Lyapunov-controlled SIR model extends standard epidemic theory by embedding feedback control laws—derived from Lyapunov stability theory—directly into transmission or intervention parameters. The core idea is simple … Read more
🧠 Conceptual Overview In the rigorous study of infectious disease dynamics, pathogens rarely circulate in isolation. The Lotka–Volterra epidemic interaction model applies principles from community ecology to epidemiology by treating distinct pathogens or viral strains as competitors for a shared resource: the susceptible host population. Within this framework, epidemic dynamics are shaped not only by … Read more
🧠 Conceptual Overview In the rigorous study of disease dynamics, the Lotka–Volterra susceptible–infected predator–prey analogy represents a powerful cross-disciplinary synthesis between epidemiology and ecology. By interpreting the infectious population as a “predator” and the susceptible population as the “prey,” this framework reframes transmission as an ecological interaction rather than a purely mechanistic process. The pathogen … Read more
🧠 Conceptual Overview In the taxonomy of mathematical epidemiology, the Logistic Growth Epidemic Model represents one of the most fundamental approaches for describing how an infectious agent spreads within a finite population. Unlike compartmental frameworks that explicitly track recovery or latency, the logistic model concentrates on the aggregate growth of infections as constrained by population … Read more
🧠 Conceptual Overview Traditional epidemic models, such as mean-field SIR systems, describe populations as homogeneous aggregates. In contrast, the Kinetic (Boltzmann-type) Epidemic Model adopts principles from statistical mechanics, modeling disease spread as the outcome of microscopic “collisions” between individuals. Each individual is characterized by a level of social activity, analogous to velocity or energy in … Read more
🧠 Conceptual Overview The Kermack–McKendrick Age-of-Infection Model represents the foundational shift from homogeneous “mean-field” assumptions to time-since-infection dynamics. Instead of treating all infectious individuals as identical, the model recognizes that transmissibility and recovery depend on the duration since infection. This infection-age structure is essential for pathogens whose infectiousness changes rapidly over time, with early peaks … Read more
🧠 Conceptual Overview While many researchers are familiar with standard compartmental ODE models, the Integral Equation Renewal Epidemic Model (Volterra) provides a more fundamental formulation of epidemic dynamics. Rather than tracking transitions between discrete compartments, this framework is built around the renewal process itself: the generation of new infections as a function of past infections … Read more