• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.1
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• pp.55-65
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• 2013

The purpose of this paper is to prove existence of solutions of an SIRS epidemic model with time delay of continuous type and the variable incidence rate and to investigate some asymptotic behaviors of the SIRS epidemic model. An example illustrating the stability of the model is given. The results extend the corresponding results in the literature.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.925-940
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• 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 Data and Information Science Society
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• v.20 no.1
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• pp.149-158
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• 2009

Tsutsugamushi fever occupies more than 80% of total fall epidemic diseases and has an incubation period of 1 or 2 weeks as well. We have assumed that the incubation period distribution is gamma and therefore, reach an agreement that the infected distribution is normal with ${\hat{\mu}}=309.92$, ${\hat{\sigma}}=14.154$ by back calculation method. The infection cases are found severely large around the month of October. The infection case distribution demonstrates the incidence number increasing rapidly and progresses fast during the month of November. In this study, we have calculated the future prevalence number of maximum 1,200 people by inferred infection probability and incubation period distribution with some sort of limitation that the trend of increasing incidence number is not taking into an account. We considered the SIRS model which is also known as epidemic model, familiar to interaction between epidemiological classes. Our estimated parameters converged well with the initial parameter values.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.635-646
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• 2012

This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1237-1248
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• 2009

The domain of attraction of a nonlinear differential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.

• Pediatric Infection and Vaccine
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• v.24 no.2
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• pp.102-107
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• 2017

Purpose: Coronary arterial lesions (CALs) were reported to have developed in children with systemic inflammatory diseases, as well as those with Kawasaki disease (KD). The purpose of this study was to confirm that the CAL development in children with KD occurs in a mouse model of sepsis presenting typical systemic inflammatory response syndrome (SIRS). Methods: To induce the sepsis mouse model with SIRS, 6-week-old C57BL/6 mice were intraperitoneally injected with endotoxin. We compared histological findings of the major organs between the control and the sepsis groups and examined CAL in the heart of the septic mice. Results: Infiltrating inflammatory cells were relatively increased in the heart, liver, and kidneys of the sepsis group, compared with those of the control group. We confirmed lymphocytic infiltration in the myocardium (myocarditis) and the pericardial soft tissue of the heart. Furthermore, coronary artery of the septic mouse was identified, but CAL was not observed. Conclusions: In this study, we failed to confirm the existence of CAL in a mouse model of sepsis. However, it is well-known that CALs are seen in many kinds of diseases that cause SIRS. Our findings suggest further investigation into the clinical significance of CAL in various systemic inflammatory diseases, including KD.