Modelling the Migration of Onchocerca volvulus in Simuliids, Using a Simple Compartmental Process

Abstract

A simple compartmental process, which is time-homogeneous and has differing transition rates between compartments, is discussed. When such a process is hierarchical, with all individuals released into the first compartment, the resulting distribution of individuals over the various compartments is multinomial. This process is applied to the migration of Onchocerca volvulus in simuliids and appears to represent successfully the early migration from the stomach through the abdomen to the thorax, provided that allowances are made for the engorgement period and the encapsulation of the blood meal by a peritrophic membrane.

Simulations of enhanced malaria transmission and host bias induced by modified vector blood location behaviour

“…The phenomenon was first described empirically in certain filariavector models (Pichon, Perrault & Laigret, 1974), which later was generalized mathematically (Prod'hon, Pichon & Riviere, 1980). Since then, non-linearities of transmission, whether facilitation or other, have been reported in other vector-parasite models (Mougey & Bain, 1976;Rosenberg, Koontz & Carter, 1982;Jerwood, Lewis & Saporu, 1984;Cabaret, 1984;Kingsolver, 1987). Facilitation itself is of potential epidemiological interest because it may lead to the establishment of three points of transmission equilibrium with different stability.…”