Ordinary Differential Equations Epidemic Models

The following sections are included:

• Simple SIRS Epidemic Models with Vital Dynamics

  • SIRS models with constant immigration and exponential death

    • SIRS models with bilinear incidence

    • SIRS models with standard incidence

  • SIRS models with logistic growth

    • Equilibrium and threshold

    • Stability analysis

    • Global stability of the equilibria for specific case: α = 0 or a = 0

• Epidemic Models with Latent Period

  • Preliminaries

    • Method I: Proving global stability using the Poincaré–Bendixson property

    • Method II: Proving global stability using autonomous convergence theorems

  • Applications

    • Application of method I

    • Application of method II

• Epidemic Models with Immigration or Dispersal

  • Epidemic models with immigration

    • SIR model with no immigration of infectives

    • SIR model with immigration of infectives

  • Epidemic models with dispersal

• Epidemic Models with Multiple Groups

  • The global stability of epidemic model only with differential susceptibility

  • The global stability of epidemic model only with differential infectivity

• Epidemic Models with Different Populations

  • Disease spread in prey–predator system

    • Disease spread only in the prey population

    • Disease spread in prey–predator populations

  • Disease spread in competitive population systems

• Epidemic Models with Control and Prevention

  • Epidemic models with quarantine

    • SIQS model with bilinear incidence

    • SIQR model with quarantine-adjusted incidence

  • Epidemic models with vaccination

    • The existence and local stability of equilibria

    • Global analysis of (2.97)

  • Epidemic models with treatment

• Bifurcation

  • Backward bifurcation

  • Hopf and Bogdanov–Takens bifurcations

    • Hopf bifurcation

    • Bogdanov–Takens bifurcations

• Persistence of Epidemic Models

  • Persistence of epidemic models of autonomous ordinary differential equations

    • Preliminaries

    • Applications

  • Persistence of epidemic models of nonautonomous ordinary differential system