Epidemic (Compartment) Models

St Susceptible Hosts, Time t

It Infectious Hosts; Initially Rare

Rt Removed Hosts

May Fix Population Size:

May Allow Host Birth, Non-Disease Mortality

Epidemic without Removal

SI Process

Only Transition: Infection Transmission

SIS Process

Two Transitions: Infection and Recovery without Immunity

Epidemic with Removal

SIR Epidemic

Two Transitions: Infection and Removal

SIRS Epidemic

Three Transitions: Infection, Removal with Immunity, Loss of Immunity

Infection Dynamics

Epidemic: Pathogen Advances from Rarity;

Infects Detectable Number of Hosts

Endemic: Dynamic Equilibrium; Constant Positive Density of Infectious Hosts

Disease-Free Equilibrium: No Infected Hosts

AND No Free-Living Pathogens

Infection Dynamics

R0 : Number of New Infections per Infection when Pathogen (Infection) Is Rare

Implies Epidemic Advance

Virulence: Reduction in Infected Host’s Fitness

Usually, Increase in Host Mortality

SIR Epidemic; Fixed Population Size

Infection Transmission

Infection - Removal

Removal

Infection Rare: Will Epidemic Occur?

SIR Epidemic: Pathogen Invasion

Growth/Decline per Infected Host at t = 0

New Infections – Removal

Calculate R0 from preceding expression.

SIR Epidemic: Pathogen Invasion

Rate of New Infection

S0 Infections/Time

Duration of Infectious Period

1/ Time

(Infections/Time) Time = New Infections

SIR Epidemic: Pathogen Invasion

Epidemic