Mathematical Models Of Zoonoses And Its Application

Zoonotic diseases can spread between humans and animals.More and more frequent contacts between them increase the probability of human suffering from zoonoses.And the zoonoses outbreak is not only a threat to human health,but also have a great impact on animal production and economics.At present,we do not comprehend completely the mechanism of the transmission of zoonotic pathogens,and we do not worked out effective intervention on the prevention and control measures for zoonotic diseases.Most emerging zoonotic pathogens originate from animals.They can directly infect humans via natural reservoirs or indirectly via intermediate hosts.Different hosts play different roles in the transmission of zoonotic pathogens.In this study we present 3 types of pathogen transmission to evaluate the effect of intermediate hosts on emerging zoonotic diseases in human epidemics.These types are identified as follows: TYPE 1,pathogen transmission without an intermediate host for comparison;TYPE 2,pathogen transmission with an intermediate host as an amplifier;and TYPE 3,pathogen transmission with an intermediate host as a vessel for genetic variation.And we established 3 mathematical models to elucidate the mechanisms underlying zoonotic disease transmission according to these 3 types.Under TYPE 1,if RN0 >1,the human epidemic would outbreak.If no intermediate host exists,the percentage of infected humans decreases as the scales of natural reservoirs decrease.Under TYPE 2 and TYPE 3,the condition RN0 >1 in natural reservoirs can determine the outbreak of zoonosis in humans;meanwhile,intermediate hosts do not possess this characteristic.In addition,when RN0 >1,an epidemic occurs.The intermediate hosts can control the peak time and number of infected humans,which is much stronger than natural reservoirs.However,the number of infected humans does not decrease as much with the same low scale of natural reservoirs.Additionally,we choose a basic model to describe the zoonotic pathogen transmission from wildlife to domestic animals and then to humans.Then we put three strategies into the basic model to control the zoonoses outbreak.Three strategies are corresponding to control measures of isolation,slaughter or similar in wildlife,domestic animals and humans respectively.We analyze the effects of these three strategies on reproductive numbers and equilibriums and we take avian influenza epidemic in China as an example to show the impacts of the strategies on emerging zoonoses in different areas at beginning.At last,we take influenza A as an example to reflect the zoonoses with human-human transmission(TYPE 1-1,TYPE 2-1)or without human-human transmission(TYPE 1-2,TYPE 2-2).And under TYPE 1-2 and TYPE 2-2,the percentage of infected humans is lower than the other two TYPEs because of no human-human transmission existing.