• Journal of applied mathematics & informatics
• /
• v.7 no.3
• /
• pp.925-940
• /
• 2000

The spatial spread of a disease in an SIRS epidemic model with immunity imparted by subclinical infection on a population has been considered. The incidence rate of infection and the rate of immunization are both of nonlinear type. The dynamics of the infectious disease and its endemicity in local and global sense have been investigated.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.45-67
• /
• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.4
• /
• pp.317-335
• /
• 2014

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1089-1099
• /
• 2010

An SIR epidemic model with pulse vaccination and time delay describing infection period is investigated. The global attractiveness of the infection-free periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Our results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease.

• Journal of applied mathematics & informatics
• /
• v.41 no.1
• /
• pp.107-121
• /
• 2023

An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.1
• /
• pp.29-62
• /
• 2018

We investigate a class of HIV infection models with two kinds of target cells: $CD4^+$ T cells and macrophages. We incorporate three distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The viruses are produced from four types of infected cells: short-lived infected $CD4^+$T cells, long-lived chronically infected $CD4^+$T cells, short-lived infected macrophages and long-lived chronically infected macrophages. The drug efficacy is assumed to be different for the two types of target cells. The HIV-target incidence rate is given by bilinear and saturation functional response while, for the third model, both HIV-target incidence rate and neutralization rate of viruses are given by nonlinear general functions. We show that the solutions of the proposed models are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the positivity and stability of the three steady states of the models. Using Lyapunov functionals, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

• Proceedings of the KOSOMBE Conference
• /
• v.1997 no.11
• /
• pp.323-326
• /
• 1997

In this study, we investigated the circardian rhythm of complexity of cardiac dynamics in humans. Dynamic 24-hour electrocardiographic recordings were obtained from 30 healthy ambulant subjects aged 41 to 50 years. or each recordings, normalized low frequency (0.04-0.1 hertz) and high frequency (>0.15 hertz) component are calculated. our different indexes obtained from separate algorithms of nonlinear dynamics - approximate entropy, correlation dimension, Lyapunov exponent and fractal dimension - were calculated. During early morning, low frequency component rose rapidly with concomitant withdrawl of high frequency component. All the our indexes of nonlinear dynamics showed remarkably same circardian rhythm: an early morning dip preceded by a steep decline during late night, a gradual recovery during evening and a peak around midnight. These data indicate that the simultansous losses of all of the our different mechanisms of nonlinear control of heart rate during early morning, concomitent with the surge of symapathetic activity and reduction of vagal activity, may contribute to the increased incidence of cardiovascular events during morning hours.