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