# مجله بین المللی محاسبات و مدل سازی ریاضی سال یازدهم شماره 2 (Spring 2021)

• تاریخ انتشار: 1400/09/15
• تعداد عناوین: 6
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• Mathematical Modeling of COVID-19 Pandemic with Treatment
Abayneh Bezabih * Page 1

In this paper, mathematical model of COVID-19 Pandemic is discussed. The positivity, boundedness, and existence of the solutions of the model equations are proved. The Disease-free & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we investigated that DFEP of the model E_0 is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ . It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.

Keywords: COVID-19, Pandemic, model, Stability Analysis, Next Generation matrix, Reproduction Number, Simulation
• Comparative Forecasting Performance of GARCH and GAS Models in the Stock Price Traded on Nigerian Stock Exchange
Oluwagbenga Babatunde *, Serifat Folorunso, Francisco Saliu Page 2

The forecasting performance of different class of volatility models was compared in this work using the daily adjusted close price of traded stocks of the Nigerian Stock Exchange (NSE) from December 10, 2013 to February 07, 2019. The GARCH and EGARCH models were selected from the GARCH models whereas the GAS and EGAS were selected from the GAS models. Two different distributions were assumed for the innovations of the volatility models and forecasts measure was obtained. Based on the forecasts measure which are Mean Error (ME) and Theil Inequality (TI) obtained, the ability the models to forecast future volatilities was achieved. The outcome of this research showed that the GAS model performed better when compared to the GARCH model under the two distributional assumptions in terms of ability to forecast future volatilities of the close price NSE stocks. However, the EGARCH performed better when student-t distribution was assumed.

Keywords: GAS Variants, innovations, Probability distribution, Forecasts Measure
• On Analytical Approach to Estimate Proceeds of Industrial Enterprises
Evgeny L. Pankratov * Page 3

In this paper we presents a model to prognosis of proceeds of industrial enterprises. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. The model gives a possibility to analyze proceeds of enterprises with account of changing of quantity of manufactured products. At the same time the model gives a possibility to take into account various expenses (raw materials, transportation costs, ...). An analytical approach for analysis of the influence of various parameters on the considered proceeds has been introduced.

Keywords: prognosis of proceeds of industrial enterprises, maximization of volume of manufactured products, analytical approach for modelling, Optimization
• Mathematical Model for the Effects of Intervention Measures on the Transmission Dynamics of Tungiasis
JAIROS SHINZEH *, Livingstone Luboobi Page 4

Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of control measures and then examine the effect of the control strategies on the transmission dynamics of Tungiasis. The model effective reproduction number is determined using the next generation operator method and the analysis is performed using the stability theory of the differential equations. The analytical results show that the disease free equilibrium is locally asymptotically stable when and unstable when . Using Meltzer matrix stability theorem we found that the disease free equilibrium is globally asymptotically stable and by Lyapunov method, the endemic equilibrium is globally asymptotically stable when . From the numerical simulation it was observed that the control strategies have positive impact on the reduction of transmission of Tungiasis disease and that they work better in combination than when applied as singly. The results from simulations will help the decision makers from national health care to advise people at risk with Tungiasis to apply the control strategies based on: educational campaign, personal protection, personal treatment, environmental hygiene and insecticides application to control the flea.

Keywords: Tungiasis, Control strategies, Steady states, Effective reproduction number, Stability, numerical simulation
• Theory of a Superluminous Vacuum Quanta as the Fabric of Space
Rajan Iyer * Page 5

Our observations of magneton with Ferrolens shows evidence pointing to such magneton entity, and more evidently in recent results with the synthetic vacuum unipole experiments. Physics formalism ansatz novel model analyses demonstrate how vacuum quanta may have sufficient energy for vacuum genesis, by constructing eigenspinors of zero_point microblackhole Hamiltonian quantum mechanics with Helmholtz decomposition matrix of gradient and rotational tensors, that are characteristic of translational vortex fields. With these mathematical physics processes, we obtain resulting energy fields spatial property partial differential equations characterizing eigenstate energetics of zero_point vacuum quagmire, as well as eigenstate vortex fields of microblackhole, both together making up plasmodial zones within quagmire. Specific eigenspinors Hamiltonian partial differential equations quantifying energy and fields eigenfunctions. Vacuum that is dipole vacuum may have superposition of complex input of quagmire vortex fields acting to create non-Hermitian quantum relativistic physics.

Keywords: quantum cosmology, Hamiltonian operator, eigenfunctions, magneton, observables, general formalism, Hamiltonian analysis, vortex eigenspinors, Gradient zero point source rotational microblackhole sink tensors
• On Fixed Point Results of L-Fuzzy Set-Valued Maps
Shehu Shagari Mohammed *, Iqra Zia, Akbar Azam Page 6

In this paper, two novel extensions of Banach and Meir-Keeler fixed point theorems for \$L\$-fuzzy set-valued map defined on a complete metric space are presented by using new general contractive conditions under suitable assumptions. In the case when the \$L\$-fuzzy set-valued map is reduced to its crisp counterparts, our obtained concepts herein generalize several significant fixed point theorems of point-to-point and point-to-set valued mappings in the comparable literature. We provide non-trivial examples to validate the hypotheses of our results.

Keywords: fuzzy set, L-fuzzy set, Fuzzy mapping, L-fuzzy mapping, fixed point, multivalued map