A mathematical model for optimising profylactic deworming strategies of companion pets moving from Echinicoccus multilocularis endemic areas to countries free of infection

Echinococcus multilocularis (Em) is a minute tapeworm residing in the small intestine of carnivores like foxes and dogs. The eggs produced forms cysts in the intermediate mice hosts and develop into the adult worms when ingested by a suitable carnivore. However, cysts may also develop in accidental intermediate hosts such as humans.

The disease, human alveolar echinococcosis, is fatal in untreated patients and results in reduced survival rates in continuously treated patients. Finland, Ireland, Malta, UK and mainland Norway consider themselves free from Em. The first case of Em was reported in Sweden in 2011.These countries therefore require dogs, cats and ferrets to be treated with an appropriate drug to prevent accidental introductions.

Ireland, UK and Malta requires dogs to be treated 24-48 hours before entry, while Sweden and Finland allow treatment up to 10 and 30 days respectively prior to entry. Such national legislations are however under pressure from the EU Commission who wants to abandon national rules to insure free movement of goods between the member states.

There is thus a need to objectively assess the risk of introducing Em to free areas in order to optimise preventive strategies while insuring national legislations does not cause unnecessary or irrational trade barriers. A qualitative import risk assessment model has been presented by EFSA. The EFSA model estimates the annual risk of importing infected dogs from an endemic area to a specific free country when taking into account the number of dogs imported, the risk of infection in the countries of origin, treatment efficacy and reinfection risk after treatment.

The EFSA model identified relatively high risk of reinfection in the Swedish and Finnish prophylactic treatment strategies. These strategies allow Praziquantel to be administrated 10 and 30 days prior to entering Sweden and Finland respectively. Because the drug is only effective 24 hours after oral intake, these strategies leaves 9 and 29 days for the dogs to be reinfected in endemic areas.

The lifespan of the worms is only 90 days and the maximum prevalence is therefore reached after 90 days exposure. A reinfection period of e.g. 9 days will thus allow for 10% of the maximum prevalence to be reached in the period between treatment and crossing the border. In the worst case the Swedish and the Finnish strategies only reduce the probability of importing an infected dog with 90% and 68 % respectively.

EFSA therefore recommended that pet animals are treated with a single dose of Praziquantel 24 to 48 hours prior to departure. The EFSA risk assessment model defines risk as the probability of introducing a dog with an Em infection. However, I suggest Em may not be so contagious that a single infected animal crossing the border necessarily will result in the successful establishment of the parasite.

A worm will produce a large number of eggs in its lifetime. But on average only very few of these eggs will result in a new adult tapeworm. And because the real concern is establishing the parasite in a free area rather than the risk of importing an infected dog, I propose risk should be defined as the number of eggs excreted in a non-endemic area.

Furthermore I suggest that the probability of establishing the parasite in a free area is linearly proportional to the number of eggs excreted in this area, and that this is a better measure of risk than the number of infected dogs crossing the border. An import risk assessment model do not differentiate between dogs with many or few worms, between long or short stays in the free area, whether the worms are egg producing or still in the immature stage or whether the worm are young or old and thus likely to have a long or short remaining lifespan.

I here present an alternative deterministic mathematical model which calculates the average number of eggs excreted in a free country by a dog exposed in an endemic area. The model quantifies the risk as the cumulative number of eggs excreted by a dog in the free country. In order to calculate the number of eggs excreted, the model calculates the probability that a dog is infected in the endemic area of exposure, and also the number of worms the dog is carrying as well as the duration each of these worms remaining lifespan together with the number of days the dog will spend in the non-endemic country.

The model also takes into account that the worms undergo a 30 days immature stage before developing into a mature egg producing stage. The model allows for a comparison of the relative risk in individual dogs with different durations of exposure in endemic areas and various durations of visits to a free country, ranging from a few hours to permanent import.

These import scenarios are then combined with various treatment strategies e.g. treatment 10 or 30 days prior to import, and even treatment several days after entering the non-endemic area. The model calculated that the number of eggs deposited in a free country was reduced the closer the treatment took place to the time of entering the free country.

But the model calculated the risk resulting from reinfection under the Swedish and Finnish treatment strategies to be relatively higher than did the EFSA model. This is because the worms potentially reinfecting the dogs after prophylactic treatment were all young and thus were expected to have a relatively long egg producing lifespan in the free country compared to the worms acquired before treatment.

While both the EFSA model and this model calculated a 90% reduction in the risk of infections in dogs when treating the dogs 10 days prior to import, this model calculated that the actual number of eggs deposited in Sweden was only reduced by 85% because the reinfecting worms produced more eggs. Somewhat counter intuitively and contrary to the EFSA risk assessment model, this model predicted that delaying treatment until arriving in free country may sometimes be highly advantageous.

Delaying treatment of Swedish dogs returning from a visit in an endemic area resulted in fewer eggs being deposited in Sweden. The shorter the duration of the stay in an endemic area the greater was the relative advantage of delaying the treatment. The benefit was very high when the stay in the endemic area was less than 30 days.

This was because returning dogs only carried the immature worm stage and therefore could not excrete eggs after returning to Sweden as long as the dogs were treated in Sweden before the worms matured to the egg excreting stage. The model suggested that e.g. a dog permanently imported from Central Europe and treated 10 days prior to entering Sweden using a 99.6% efficient drug on average would deposit 400 million times as many eggs and hence constitute a 400 million times higher risk than a treated Danish dog passing Sweden in four hours transit.

This is a much higher difference than would be estimated by a traditional import risk assessment model. This is because import risk assessment focus on the difference in infection incidence in the two endemic areas of exposure, but ignores that infected dogs from high risk areas also have higher worm burdens and ignores that dogs in transit have much shorter time in the free country to deposit eggs than dogs permanently imported, and finally ignores that reinfecting worms remains in the immature stage during transit while they will eventually mature and excrete eggs in permanently imported dogs.

The only eggs that dogs in transit may deposit will therefore originate from the few worms surviving treatment due to treatment failure. Because we do not know the actual risk of establishing the infection caused by each deposited egg the model cannot quantify the risk. But the model allows for relative quantitative comparisons of different import scenarios, endemicity levels, drug efficiencies and treatment strategies, and can thus be useful for optimising national preventive measures in an objective and transparent way.