Table 1.
Definition of the model parameters. i = T or U.
| parameter | meaning |
|---|---|
| ki | biting rate, i.e. the number of bites per unit time on hosts from group i an individual vector has |
| Ni | host group i population size |
| V | vector population size |
| r | vector fixed birth rate |
| N | the total host population size, i.e. N = Nu + NT |
| pi | the efficiency that an infected vector would infect a susceptible individual of host group i during one feeding event |
| qi | the efficiency that an infected individual of host group i would infect a susceptible vector during one feeding event |
| δi | recovery rate of host in group i, i.e. 1/δi is the infectiousness duration |
| d | vector death rate for coverage rate x (i.e. d is a function of x) |
| d0 | basal vector death rate, i.e. death rate without treatment or without killing effect |
| k | the total biting rate of the vector, i.e. the number of bites per unit time of individual vector on the entire host population, i.e. k = kU + kT |
| gi | the transmission ability of hosts in group i. gi = piqi/δi |
| L | vector latent period |
| x | the treated population proportion, i.e. NT = xN and NU = (1 − x)N |
| hi1 | post-biting handling time. The time the vector needs to handle a host from group i after a successful biting attempt |
| hi2 | pre-biting handling time. The time the vector spends when occupying with host individual of group i before biting it |
| hi | the total handling time of host on group i. The amount of time the vector needs to spend in handling hosts of group i in order to achieve a single bite |
| bi | the protection time. The average time units the vector needs for a successful biting attempt on host group i individual |
| Ai | the general searching efficiency, the number of bites per unit time on host group i incurred by a vector that forages in host i population with unit density (Ni = 1) and zero handling times |
| ai | host i searching efficiency. The attractiveness of hosts belong to group i |
| βi | the probability that the vector would successfully bite an individual from host group i |
| η | a constant that determines the ability of a treatment to increase the vector death rate, or alternatively, decrease its life expectancy |