• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1017-1035
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• 2023

In this paper, we construct a monkeypox model which is similar to smallpox infection. It is caused by a monkeypox virus which is related to Poxviridae family. It will occur mostly in West African communities and in remote Central. We develop a system of differential equations for an SEIR (Suspected, Exposed, Infected and Recovered) model and analyze the outbreak of monkeypox disease and its effect on United States(US) population. We establish theorems on asymptotical stability conditions for endemic equilibrium and disease-free equilibrium. The basic reproduction number R₀ has been determined using next generation matrix. We expect that this study will be effective at controlling monkeypox spread in United States. Our goal is to see whether monkeypox can be controlled and destroyed by smallpox vaccination. We find that monkeypox is controllable and can be fully destroyed in disease free state by vaccination. However, in the endemic state, monkeypox cannot be destroyed by vaccination alone.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.685-699
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• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• 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.

• 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.

• 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.