We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in deta...We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.展开更多
In the real world, quite a few infectious diseases like schistosomiasis spread seasonally. In this paper, a nonautonomous schistosomiasis system is established, in which the saturation incidence rate and the coefficie...In the real world, quite a few infectious diseases like schistosomiasis spread seasonally. In this paper, a nonautonomous schistosomiasis system is established, in which the saturation incidence rate and the coefficients varying with time are taken into account. The long-time behavior of the model is studied. Under quite weak assumptions, sufficient conditions for the permanence and extinction of infectious population of disease are obtained. Finally, numerical simulations illustrate the validity of our results.展开更多
基金supported by National Natural Science Foundations of China (Grant Nos. 10771216 and 11071259)
文摘We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.
基金Special thanks to the anonymous referees who have given us very useful suggestions. The research has been supported by the Natural Science Foundation of China （11261004）, the National Key Technologies R＆D Program of China （2009BAI78B01） and the Science and Technology Plan Projects of Jiangxi Provincial Education Department （GJJ14665, GJJ14673）.
文摘In the real world, quite a few infectious diseases like schistosomiasis spread seasonally. In this paper, a nonautonomous schistosomiasis system is established, in which the saturation incidence rate and the coefficients varying with time are taken into account. The long-time behavior of the model is studied. Under quite weak assumptions, sufficient conditions for the permanence and extinction of infectious population of disease are obtained. Finally, numerical simulations illustrate the validity of our results.
