Infectious Disease Dynamics

Misc

Origin of Viruses

Virus-first

Reduction

Escape

Transitions in human IDD history

10 000

1000

100

Assumptions

Constant Parameters

Λ

Reasonable as birth rate if the population remains close to constant over the relevant timeframe

Simplest way to achieve equilibration to constant population size

Can be a function of population sizes

β

Often times, does not make sense as a constant

𝛿

Lifespan is exponentially distributed with mean = 1/𝛿

Mass action kinetics

Transmission is proportional to SI

Assumes well mixed all types, unstructured population

Density dependence

S and I Refer to densities in some are ( Like concentrations), import for mass-action assumption.

This is acceptable when one expects the rate of infection to increase with the density, however for examples like STDs, where the density of people doesn't really increase the amount of sexual partners, this assumption maybe less realistic

Homogeneity of Host classes

Everyone in a host class is the same

This breaks down quite easily as people of differing ages, sexes... have differing characteristics

SIR model

SEIR

SIRS

Adds a exposed but not infectious compartment, makes sense for disease like rabies, which have a long incubation periods

Adds flow from Recovered back to Suspectable, makes sense when immunity is not lifelong as in true for most disease

Eq for S is the same is in the SIR model, because the added flow in is compensated for by more flow to I

Rabies example

System exhibits Oscillations because of the delay in exposure and the point in time when the become infectious

Vaccination effectively shrinks S, which reduces carrying capacity

K is the carrying capacity

Chapter 3

R0

Ways of estimating R0

Reported Cases

If we assume that the disease has little effect on total populations size we can manipulate the expression for the I_endemic to get a term from R0 of the form 1-1/R0 . (We also need birth, death and recovery rates. This leads to a low confidence level on this estimate.

Initial dynamics

Early on in an epidemic S_f is the same as S, knowing that we manipulate the term for dI/dt to get R_0 and then solve the differential equation and fit it to data. For this we need atleast two timepoint, early in the pandemic as well as estimates for death and recovery rates. Another problem is that early on, stochastics effects will dominate counts

R0 = 1+L/A

If all the assumptions of the age of infection vs life expectancy hold, we can use measurements for those to estimate R0

Chapter 4

Vaccine efficacy

VEs = 1-pv/p0