## Explanatory models

 EXPLANATORY MODELS
• Mathematical models that describe the dynamics (i.e.biological processes) of parasite and host populations have been formulated.
• These more refined techniques allow the course of a disease to be simulated.
• They include models for forecasting fluke morbidity, the air borne spread of foot and mouth disease and the occurrence of clinical Ostertagiosis.

Example: Bovine Ostertagiosis

• The level of pasture contamination by infective Ostertagia ostertagi larva can be predicted by simulating the course of events experienced by cohorts of parasite eggs deposited on pasture.
• This involves estimating the proportion of eggs that proceed to the first, second and third larval stages using development fractions, which quantify the rate of development of the parasite from one stage to next stage according to the temperatures that it experiences.
• In addition parameters associated with infectivity, fecundity and migratory behaviour of the larvae must be included.

A = (K-Ao) (1-e-αL) + Ao

• A= Number of adult worms expected in the abomasum of that calf after 21 days of infection
• Ao = Number of adult worms already in the abomasum
• The parameters K and α control the rate of establishment so that the proportion established is high for low levels of challenge and low for high levels of challenge.
• The number of eggs, E produced after 21 days is estimated from empirical data relating to egg output to adult worm burden. These eggs undergo development.
• The time to the appearance of infective larvae is estimated by calculating from daily temperatures, the fraction of development to take place each day and summing these fractions until allow development has occurred ‘n’ days later.

1/D1+1/D2+….1/Dn = 1

• Where the ‘Ds’ are the number of days that would be required to complete development under conditions of constant temperature.
• Adding ‘n’ to 22 day gives the earliest day on which the infective larvae can appear.
• Not all developing eggs and larvae survive and so the number of eggs that avoid mortality is the proportion, ‘pn’ of the egg output on 22nd day.
• The parameter ‘p’ is an estimate of the daily survival rate.
• If the values of ‘n’ and ‘pn’ are determined for each day during which the calf grazes, then it is possible to estimate the expected totals of infective larvae on pasture and number of adult worms infecting the calf.
• A prediction of herbage infective larval burdens using this type of simulation model can facilitate optimum use of anthelmintics and movement of animals to safe pasture before challenge large number of infective larvae, thereby preventing clinical Ostertagiosis.
Last modified: Wednesday, 16 May 2012, 5:09 AM