• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.1-25
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• 2013

In this paper we have developed a mathematical model of alcohol abuse. It consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined. Sensitivity analysis of $R_0$ identifies ${\beta}_1$, the transmission coefficient from moderate and occasional drinker to heavy drinker, as the most useful parameter to target for the reduction of $R_0$. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0$ < 1. It is found that, when $R_0$ = 1, a backward bifurcation can occur and when $R_0$ > 1, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE. Our aim of this analysis is to identify the parameters of interest for further study with a view for informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.747-767
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• 2013

In this paper we have constructed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined and sensitivity analysis of $R_0$ indicates that ${\beta}1$ (the transmission coefficient from moderate and occasional drinker to heavy drinker) is the most useful parameter for preventing drinking habit. Stability analysis of the model is made using the basic reproduction number. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0&lt;1$. It is found that, when $R_0=1$, a backward bifurcation can occur and when $R_0&gt;1$, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE under some conditions. Our important analytical findings are illustrated through computer simulation. Epidemiological implications of our analytical findings are addressed critically.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1097-1115
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• 2011

We consider the global stability of a general tuberculosis model with two differential infectivity, n classes of latent individuals and mass action incidence. This system exhibits the traditional threshold behavior. There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction ratio $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0$ > 1), or infection-free ($\mathcal{R}_0{\leq}1$). The global stability of this model is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Both the analytical results and numerical simulations suggest that patients should be strongly encouraged to complete their treatment and sputum examination.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.517-528
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• 2012

This paper is estimating the domain of attraction for a class of susceptible-exposed-infectious-recovered (SEIR) epidemic dynamic models by using sum of squares optimization. First, the stability is analyzed for the equilibriums of SEIR model, and the domain of attraction in the endemic equilibrium is estimated by using sum of squares optimization. Finally, a numerical example is examined.

• 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.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.131-158
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• 2024

This study investigates the impact of precautionary measures, such as isolating exposed individuals, wearing masks, and maintaining physical distance, on preventing infectious disease. A deterministic SEIQHRV epidemic model is employed for this purpose. The model's positivity, boundedness, disease-free, and endemic equilibrium points are identified. A sensitivity test assesses the impact of preventive measures on infected classes. Results show that a basic reproduction number less than unity drives disease eradiction, while a higher unity value encourages the adoption of preventive measures.

• Environmental Engineering Research
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• v.25 no.3
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• pp.384-392
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• 2020

The presence of high fluoride concentration (> 1.5 mg/L) in water causes serious health problems such as fluorosis, infertility, brain damage, etc., which are endemic to many places in the world. This study has investigated the fluoride removal capacity of the novel activated biochar (BTS) and hydrochar (HTS) using Teff (Eragrostis tef) straw as a precursor. Activated biochar with mesoporous structures and large specific surface area of 627.7 ㎡/g were prepared via pyrolysis process. Low-cost carbonaceous hydrochar were also synthesized by an acid assisted hydrothermal carbonization process. Results obtained from both adsorbents show that the best local maximum fluoride removal was achieved at pH 2, contact time 120 min and agitation speed 200 rpm. The thermodynamic studies proved that the adsorption process was spontaneous and exothermic in nature. Both adsorbents equilibrium data fitted to Langmuir isotherm. However, Freundlich isotherm fitted best for BTS. The maximum fluoride loading capacity of BTS and HTS was found to be 212 and 88.7 mg/g, respectively. The variation could primarily be attributed to a relatively larger Surface area for BTS. Hence, to treat fluoride contaminated water, BTS can be promising as an effective adsorbent.

• Animal cells and systems
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• v.16 no.4
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• pp.321-328
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• 2012

The oily bittering Acheilognathus koreensis is a freshwater species that is endemic to Korea and is experiencing severe declines in natural populations as a result of habitat fragmentation and water pollution. For the conservation and restoration of this species, it is necessary to assess its genetic diversity at the population level. We developed 13 polymorphic microsatellite loci that were used to analyze the genetic diversity of two populations collected from the Kum River and the Tamjin River in Korea. All loci exhibited Mendelian inheritance patterns when examined in controlled crosses. Both populations revealed high levels of variability, with the number of alleles ranging from 3 to 20 and observed and expected heterozygosities ranging from 0.500 to 0.969 and from 0.529 to 0.938, respectively. None of the loci showed significant deviation from Hardy-Weinberg equilibrium, and one pair of loci showed significant linkage disequilibrium after Bonferroni correction. Pairwise $F_{ST}$ and genetic distance estimation showed significant differences between two populations. These results suggest that the microsatellites developed herein can be used to study the genetic diversity, population structure and conservation measure of A. koreensis.

• Parasites, Hosts and Diseases
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• v.23 no.2
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• pp.241-246
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• 1985

The epidemiological status of ascariasis was analyzed in 8 rural villages in Korea, through observation of its epidemiological parameters such as prevalence, worm burden and basic reproductive rate. Total 978 inhabitants were subjected to stool examination and recovery of worms after chemotherapy with pyrantel pamoate. The results were as follows: 1. The worm positive rate in each village was 16.5~79.5%, while the egg positive rate was 9~18% lower, 3.3~66.7%. The average worm burden (among all inhabitants) ranged from O. 21 to 8. 44 by villages and the frequency of cases with each worm burden showed negative binomial distributions with 'k' values of O. 38-0. 54. 2. The prevalence rates (worm) in each village was almost identical with the theoretical ones from Anderson and May's equation; $p=1-(1+M^*/k)^{-k}$, where 'p' is worm prevalence and '$M^*$' equilibrium average worm burden. The basic reproductive rate 'R' was calculated from 1.03 to 2.11. lt is suggested that, although 'R' in lower endemic areas is approaching to the breakpoint of reinfection (R=1), control programs of ascariasis in Korea should be continued until it becomes below the level nationwidely.