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Ünite 4: Epidemic — Kavram Eşleştirme

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Susceptible — Refers to individuals within a population who do not have immunity and can potentially contract an infectious disease upon coming into contact with an infected person. In the mean-field model, their fraction is represented mathematically as 1 - u - v.

Infected — Represents individuals who currently carry the infectious disease and are actively capable of transmitting it to susceptible neighbors. In differential equations, their fraction is denoted by the variable u.

Removed — Denotes individuals who have either recovered from the infection, gained immunity, or been isolated, represented by the variable v in epidemic simulation models. Depending on model parameters, these individuals may stay immune or eventually return to the susceptible pool.

Mean-Field Approximation — A simplifying assumption in epidemic modeling that considers the population to be large, uniformly mixed, and homogeneous, ignoring individual spatial locations and local interaction networks. It allows the system dynamics to be expressed using ordinary differential equations.

Cellular Automaton — A discrete modeling technique consisting of a grid of cells that evolve through a set of simple local rules over discrete time steps, often used to simulate spatial epidemic spread without heavy differential calculations.

Stochastic Dynamics — Probabilistic modeling techniques, including agent-based simulations, random walks, and Monte-Carlo methods, that incorporate randomness into the study of epidemic transmission and social system dynamics.

Critical Value of Delta (delta_c) — A specific threshold value for the recovery/removal parameter delta ($\delta$). When $\delta < \delta_c$, the epidemic spreads linearly with time before reaching its steady-state distribution, whereas larger values cause the outbreak to die out.

Spatial Distribution — The geographic arrangement and dispersion of individuals across a physical area. Incorporating spatial distribution is vital because mean-field models fail to capture localized geographic barriers and movement speeds, such as the 150-meter-per-week measles propagation.

Partial Differential Equation Approach — A mathematical modeling framework that extends ordinary differential equations by explicitly incorporating spatial coordinates and population density $P(x, t)$, approximating random walk behaviors and linear spread rates.

Random Walk — A mathematical formalization of a path that consists of a succession of random steps, which is closely approximated by the solutions of partial differential equations used in spatial epidemic modeling.