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
In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells...In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intraeellular delay only when self-proliferation of activated CD4＋T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4＋T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4＋T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4＋T cells and virus particles in the blood plasma of HIV patients.展开更多
基金Supported by the National Science Foundation of the Education Depart ment of Henan Province (2010B11021)the Young Backbone Teacher Foundation of Xinyang Normal University
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.
文摘In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intraeellular delay only when self-proliferation of activated CD4＋T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4＋T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4＋T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4＋T cells and virus particles in the blood plasma of HIV patients.
