The emergence of any new infectious disease poses much stress on the government to control the spread of such disease. The easy, fast and less expensive way to slow down the spread of disease is to make the population...The emergence of any new infectious disease poses much stress on the government to control the spread of such disease. The easy, fast and less expensive way to slow down the spread of disease is to make the population be aware of its spread and possible control mechanisms. For this purpose, government allocates some funds to make public aware through mass media, print media, pamphlets, etc. Keeping this in view, in this paper, a nonlinear mathematical model is proposed and analyzed to assess the effect of time delay in providing funds by the government to warn people. It is assumed that suscep- tible individuals contract infection through the direct contact with infected individuals; however the rate of contracting infection is a decreasing function of funds availability. The proposed model is analyzed using stability theory of delay differential equations and numerical simulations. The model analysis shows that the increase in funds to warn people reduces the number of infected individuals but delay in providing the funds desta- bilizes the interior equilibrium and may cause stability switches.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
文摘The emergence of any new infectious disease poses much stress on the government to control the spread of such disease. The easy, fast and less expensive way to slow down the spread of disease is to make the population be aware of its spread and possible control mechanisms. For this purpose, government allocates some funds to make public aware through mass media, print media, pamphlets, etc. Keeping this in view, in this paper, a nonlinear mathematical model is proposed and analyzed to assess the effect of time delay in providing funds by the government to warn people. It is assumed that suscep- tible individuals contract infection through the direct contact with infected individuals; however the rate of contracting infection is a decreasing function of funds availability. The proposed model is analyzed using stability theory of delay differential equations and numerical simulations. The model analysis shows that the increase in funds to warn people reduces the number of infected individuals but delay in providing the funds desta- bilizes the interior equilibrium and may cause stability switches.
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.
