International Journal of Mathematical Modelling & Computations
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International Journal of Mathematical Modelling & Computationsendaily1Fri, 25 Jun 2021 00:00:00 +0430Fri, 25 Jun 2021 00:00:00 +0430Mathematical Model for the Effects of Intervention Measures on the Transmission Dynamics of Tungiasis
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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 &ldquo;Tunga penetrans&rdquo; 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.Comparative Forecasting Performance of GARCH and GAS Models in the Stock Price Traded on Nigerian Stock Exchange
http://ijm2c.iauctb.ac.ir/article_684813.html
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.On Fixed Point Results of L-Fuzzy Set-Valued Maps
http://ijm2c.iauctb.ac.ir/article_684814.html
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.Mathematical Modeling of COVID-19 Pandemic with Treatment
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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 &amp; 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 &alpha;&le;&beta;+&delta;+&mu; &amp; unstable if &alpha;&gt;&beta;+&delta;+&mu; . 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.Local existence and blow up of solutions for a system of viscoelastic wave equations of Kirchhoff type with delay and logarithmic nonlinearity
http://ijm2c.iauctb.ac.ir/article_684816.html
In this paper, we consider a system of viscoelastic wave equations of Kirchhoff type with delay
and logarithmic nonlinearity. We obtain the local existence of solution by using the Faed-Galerkin approximation and under suitable conditions, we prove the blow up of solutions in finite time.Impact of Antiviral Treatment of Avian Influenza in Poultry Farm
http://ijm2c.iauctb.ac.ir/article_684817.html
In the present paper, we have focused on the antiviral treatment of avian influenza to predict the situation of the disease and analyzed the stability of the model at the equilibrium points (disease-free and endemic). In this concern, we have applied the SITR model based on the well-known SIR model to calculate the basic reproduction number and final size relation. Important parameters, such as susceptible, infective, treatment, and removal (SITR) rate under the compartmental method have been studied theoretically. The analytical results highlight that the model results are locally and globally stable at disease-free equilibrium if the basic reproduction number is less than one and it is locally and globally stable at endemic equilibrium if the basic reproduction number is greater than one. The numerical simulations of the developed model (SITR) are performed graphically with the help of the Range-Kutta method and we have also observed that each compartment has much affected by the infection and death rate, whereas re-susceptive has no significant effect on compartments.On D-efficiency of Reduced Models for Central Composite Experimental Designs Within a Split-plot Structure
http://ijm2c.iauctb.ac.ir/article_684818.html
Choosing a response surface design to fit certain kinds of models is a difficult task. Extensive research comprising a collection of efficient second-order response surface designs from which a researcher may choose to best fit his/her needs has been conducted, which are based solely on a widely-accepted assumption of a completely randomized error structure of statistically-designed experiments. However, this assumption is not feasible in industrial experiments, which are often split-plot in nature and for which randomization of some factors have to be restricted due to certain constraints. The performance of such experimental designs depends strongly on the relative magnitude (d) of the whole-plot and sub-plot error variances. This work focuses on reduced second-order models having one, two, or all of their quadratic and/or interaction terms removed from the full models of some chosen candidate split-plot central composite designs (CCDs). It investigates the effects of model reduction on efficiency of these designs by computing the relative D-efficiencies for the formulated reduced models with respect to their corresponding full designs and assessing the efficiency losses under specific values of d. The study revealed a significant loss of D-efficiency in these designs, which depend strongly on the removed term(s) and increases, across all values of d, as the number of whole-plot factors increases.Review and Modelling of Hexavalent Chromium Removal Efficiency of Bio-Sorption and Activated Carbon for Waste Water Treatment
http://ijm2c.iauctb.ac.ir/article_684819.html
Hexavalent chromium pollutants in water are the most challenging of human health according to current situations. From many treatment methods, the adsorption method is the best alternatives for hexavalent chromium removal from wastewater. Activated carbon and biosorption are the basic adsorbents in the adsorption process. In these review and model optimization there where many articles reviewed under activated carbons and biosorption without carbonizing. The basic factors for the two adsorbents are adsorbent dose, pH value, and contact time at around room temperature. Maximum removal efficiency allocated at the acidic condition, these show the &ndash;OH releasing state is at the acidic condition. According to articles reviewed, the efficiency of bio- sorbent was greater than activated carbon. There were similarity adsorption efficiency of activated carbon and biosorption. As reviewed activated carbon and biosorption preparation, activated carbon preparation was more energy consumption than biosorption preparations. The model optimization also summarised and optimum condition of maximum removal efficiency where specified.General anti-angiogenic therapy protocols with chemotherapy
http://ijm2c.iauctb.ac.ir/article_684821.html
This given paper can be considered as a continuation of previous work, doing on cancer models
and their control by a set-valued method, in the context of viability theory. We analyze a class
models of ordinary differential equations, taking into account the possibility to directly acting
on tumor. However we can augment the class by a simple ordinary differential equation of the
tumor control term, and join it to the other variables state. This will allow to exploit results
to generalize the approach.On Analytical Approach to Estimate Proceeds of Industrial Enterprises
http://ijm2c.iauctb.ac.ir/article_684822.html
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.A solution towards to detract cold start in recommender systems dealing with singular value decomposition
http://ijm2c.iauctb.ac.ir/article_684824.html
Recommender system based on collaborative filtering (CF) suffers from two basic problems known as cold start and sparse data. Appling metric similarity criteria through matrix factorization is one of the ways to reduce challenge of cold start. However, matrix factorization extract characteristics of user vectors &amp; items, to reduce accuracy of recommendations. Therefore, SSVD two-level matrix design was designed to refine features of users and items through NHUSM similarity criteria, which used PSS and URP similarity criteria to increase accuracy to enhance the final recommendations to users. In addition to compare with common recommendation methods, SSVD is evaluated on two real data sets, IMDB &amp;STS. Experimental results depict that proposed SSVD algorithm performs better than traditional methods of User-CF, Items-CF, and SVD recommendation in terms of precision, recall, F1-measure. Our detection emphasizes and accentuate the importance of cold start in recommender system and provide with insights on proposed solutions and limitations, which contributes to the development.Anisotropic Charged Stellar Models
http://ijm2c.iauctb.ac.ir/article_684825.html
A new class of exact solutions of the Einstein-Maxwell system is found in closed form for a static spherically symmetric anisotropic star in the presence of an electric field by generalizing earlier approaches. The field equations are integrated by specifying one of the gravitational potentials, the anisotropic factor and electric field which are physically reasonable. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system in the form of series with anisotropic matter. For specific parameter values it is possible to find new exact models for the Einstein-Maxwell system in terms of elementary functions from the general series solution. Our results contain particular solutions found previously including models of Thirukkanesh and Maharaj (2009) and Komathiraj and Maharaj (2007) charged relativistic models.The Bivariate Modified Exponential Geometric Distribution: model, properties and applications
http://ijm2c.iauctb.ac.ir/article_684826.html
In this paper, we have introduced a fiveâparameter bivariate model by taking a geometric minimum of the modified exponential distributions. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. A number of simulation experiments have been performed to determine the effectiveness of the proposed EM algorithm. We analyze two datasets for illustrative purposes, and it is observed that the proposed models and the expectationâmaximization algorithm perform at a satisfactory level.COVID-19 dynamics in Africa under the influence of asymptomatic cases and re-infection
http://ijm2c.iauctb.ac.ir/article_684827.html
Since December 2019 that the coronavirus pandemic (COVID-19) has hit the world, with over 13 million cases recorded, only a little above 4.67 percent of the cases have been recorded in the continent of Africa. The percentage of cases in Africa rose significantly from 2 percent in the month of May 2020 to above 4.67 percent by the end of July 15, 2020. This rapid increase in the percentage indicates a need to study the transmission, control strategy, and dynamics of COVID-19 in Africa. In this study, a nonlinear mathematical model to investigate the impact of asymptomatic cases on the transmission dynamics of COVID-19 in Africa is proposed. The model is analyzed, the reproduction number is obtained, the local and the global asymptotic stability of the equilibria were established. We investigate the existence of backward bifurcation and we present the numerical simulations to verify our theoretical results. The study shows that the reproduction number is a decreasing function of detection rate and as the rate of re-infection increases, both the asymptomatic and symptomatic cases rise significantly. The results also indicate that repeated and increase testing to detect people living with the disease will be very effective in containing and reducing the burden of COVID-19 in Africa.Advanced Refinements of Numerical Radius Inequalities
http://ijm2c.iauctb.ac.ir/article_684828.html
By taking into account that the computation of the numerical radius is an optimization problem, we prove, in this paper, several refinements of the numerical radius inequalities for Hilbert space operators. It is shown, among other inequalities, that if $A$ is a bounded linear operator on a complex Hilbert space, then
[omega left( A right)le frac{1}{2}sqrt{left| {{left| A right|}^{2}}+{{left| {{A}^{*}} right|}^{2}} right|+left| left| A right|left| {{A}^{*}} right|+left| {{A}^{*}} right|left| A right| right|},]
where $omega left( A right)$, $left| A right|$, and $left| A right|$ are the numerical radius, the usual operator norm, and the absolute value of $A$, respectively. This inequality provides a refinement of an earlier numerical radius inequality due to Kittaneh, namely,
[omega left( A right)le frac{1}{2}left( left| A right|+{{left| {{A}^{2}} right|}^{frac{1}{2}}} right).]
Some related inequalities are also discussed.Apply new optimized MRA& invariant solutions on the generalized-FKPP equation
http://ijm2c.iauctb.ac.ir/article_684829.html
So far, the numerous methods for solving and analyzing differential equations are proposed. Meanwhile; the combined methods are beneficial; one of them is the Optimized MRA method (OMRA). This method is based on the Father wavelets (dependent on the invariant solutions obtained by the Lie symmetry method) and correspondent MRA. In this paper, we apply the OMRA on the generalized version of FKPP equation (GFKPP) with function coefficient
begin{eqnarray*}
f u_{tt}(x,t) + u_t(x,t) = u_{xx}(x,t) + u(x,t) - u^2(x,t),
end{eqnarray*}
where $f$ is a smooth function of either $x$ or $t$.
We will see that by the suitable Father wavelets, this method proposes attractive approximate solutions.Theory of a Superluminous Vacuum Quanta as the Fabric of Space
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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.Numerical Solution of nonlinear system of ordinary differential equations by the Newton-Taylor Polynomial and Extrapolation with application from a Corona Virus model
http://ijm2c.iauctb.ac.ir/article_685126.html
In this paper, we consider a nonlinear non autonomous system of differential equations.
We linearize this system by the Newton&#039;s method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positive real l&gt;0 . For this purpose, in the first step we solve the problem on [0,l]. By knowing the solution on [0,l], we solve the problem on [l,2l] and obtain the solution on [0,2l]. We continue this procedure until [0,Nl]. In each partial interval [(k-1)l,kl], first of all, we solve the problem by the extrapolation method and obtain an initial guess for the Newton-Taylor polynomial solutions. These procedures cause that the errors don&rsquo;t propagate. The sequence of linear systems in Newton&#039;s method are solved by a famous method called Taylor polynomial solutions, which have a good accuracy for linear systems of ODE. Finally, we give a mathematical model of the novel corona virus disease and illustrate accuracy and applicability of the method by some examples from this model and compare them by similar work, that simulate the numerical solutions.Stability analysis of a staged progression susceptibility model for infectious diseases
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The aim of this paper is to provide a stability analysis for models with a general structure and mass action incidence; which include stage progression susceptibility, differential infectivity as well, and the loss of immunity induced by the vaccine also. We establish that the global dynamics are completely determined by the basic reproduction number $R_0$. More specifically, we prove that when $R_0$ is smaller or equal to one, the disease free equilibrium is globally asymptotically stable; while when it is greater than one, there exist a unique endemic equilibrium. We also provide sufficient conditions for the global asymptotic stability of the endemic equilibrium.