Runge–Kutta pairs suited for SIR‐type epidemic models
Vladislav N. Kovalnogov, Theodore E. Simos, Ch. Tsitouras
Abstract
Modeling the infectious diseases concludes in systems of ordinary differential equations (ODEs). The compartments in these equations (e.g., the numbers of susceptible, infectious, or immunized individuals) change in time. The ODEs arriving in these models are quadratic. Thus, we may apply special type of Runge–Kutta (RK) pairs for solving them. Here, we construct a new RK pair of orders five and four that is special tuned for this type of ODEs. Its superiority over standard RK pairs from the literature is illustrated when applied to various epidemic models, valid in measuring COVID‐19 spread.
Topics & Concepts
OdeMathematicsOrdinary differential equationRunge–Kutta methodsType (biology)Quadratic equationApplied mathematicsConstruct (python library)Epidemic modelDynamical systems theoryDifferential equationCalculus (dental)Mathematical analysisComputer scienceGeometryDemographyPopulationSociologyQuantum mechanicsPhysicsDentistryEcologyBiologyMedicineProgramming languageMathematical and Theoretical Epidemiology and Ecology ModelsFractional Differential Equations SolutionsNumerical methods for differential equations