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Quantitative disease models can explain …
when we see lone epidemics vs repeated cycles vs epidemic disease, by predicting when and why parasites invade, spread and persist
Compartment models allows us to …
relate processes and mechanisms (e.g transmission'; recovery) to patterns (e.g case numbers; data; infection prevalence)
What are the basic aims of the compartmental model?
classify host individuals in a population according to their infection status
identify and quantify the processes that cause individuals to move to a new status
what does the speed at which individuals move between compartments (rate) tell us?
how long they spend (period of time) in a compartment
(assuming no host reproduction, death, or virulence)
transmission between hosts require:
contact between a host and a parasite, the “right” sort of contact needs to occur, parasite needs to establish
density-dependent transmission:
contact rate between individuals increases with density of hosts (often assume a linear relationship)
threshold population size for invasion exists
R0 increases with N
c*N (also known as β)
transmission rate (contact between individuals)
S/N*I
the “right” sort of contact needs to occur between a S and an I individual
a
parasite needs to establish -
expression for density dependent transmission between hosts:
βSI
γ
recovery rate (per-capita recovery rate)
infectious period:
the length of time that an individual is capable of transmitting infection to susceptible individuals
1/γ
infectious period
R0
the net reproductive rate of a parasite
R0 will vary because of variation in:
the rate of transmission due to the variation in the probability of parasite establishment or the slope of the relationship between the contact rate and N
the recovery rate
the initial density of susceptible
frequency-dependent transmission:
contact rate does not increase with host density
no threshold population size for invasion
R0 does not depend on N
