The threat was one of the reasons why the southern saltmarsh mosquito, which came here through the Port of Napier in the late 1990s, was eradicated after 10 years of effort and at a taxpayer cost of about $71m.
Nearly three out of five known infectious diseases in humans across the world were estimated to be caused by pathogens that were zoonotic, or those that can be shared with humans and animals.
Further, around three-quarters of the new diseases emerging to date were zoonotic, and their emergence was closely linked with environmental change and agricultural intensification.
"New Zealand has been a land of milk and honey for the rats, which were introduced largely unwittingly, and possums introduced in the 19th Century to establish a fur industry," University of Otago public health researcher Dr Mary McIntyre said.
"We have a moderate climate, abundant food, and possums have few natural enemies."
What's more, and in contrast to their native Australia, the possums averaged a kilogram heavier - and gave birth twice a year in New Zealand.
The spread of diseases was largely a cost to society of our globalising travel habits, which greatly increased the chances of spreading new pests such as mosquitoes and ticks, McIntyre said.
Travel also increased the spread of pathogens carried by people – who may or may not know they are infected.
The establishment of mosquito-borne disease by infected people was a particular concern here, since there are already mosquitoes in New Zealand which carried infections.
One of these was a minor vector of Dengue virus in Australia, and scientists believe this could work together with related Australian or Pacific mosquitoes to spread zika or chikungunya virus, should these mosquitoes ever come here.
"In the right conditions people travelling from overseas could infect the local mosquitoes – instead of the other way around."
"Global warming increases chances of this as higher temperatures increase reproduction of the disease carriers such as rats and insects, as well as increasing the rates at which a pathogen multiplies inside an insect such as a mosquito or tick."
Warmer climates also assisted the spread of carriers such as rodents and mosquitoes, with the pathogens they carry, into areas that were previously too cool for their numbers to build up to levels where infection would be transmitted.
Back to pest predators, McIntyre said the mass fruiting and seeding of some native forest and grassland vegetation brought another threat, as it could dramatically boost rodent populations, which in turn built up numbers of their predators.
Eradicating them wouldn't just take a large number of vectors for human disease out of play, but remove the need to use 1080 poison for pest control.
"We believe it is in everyone's interests to support the eradication of these introduced creatures, not just for the sake of New Zealand's native plants and animals, but also for the health concerns of our human population," McIntyre said.
The nationwide effort is being led in a partnership between Government agencies and Predator Free New Zealand Limited, a $28m company to identify large pest control programmes and attract private investment.
Scientists working under the New Zealand's Biological Heritage National Science Challenge, and other efforts, are also hunting for solutions to wipe out pests.