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आयतन 9, मुद्दा 4 (2020)


Numerical Approach for Determining Impact of Steric Effects in Biological Ion Channel

Abidha Monica Gwecho*, Wang Shu and Onyango Thomas Mboya

Flow through biological ion channel is understandably complex to support numerous and vital processes that promote life. To account for the biological evolution, mathematical

modelling that incorporates electrostatic interaction of ions and effects due to size exclusion has been studied, conceivably with element of difficulty and inaccuracy. In this

paper the Nernst-Planck(NP) equation for ion fluxes that uses Lennard Jonnes(LJ) potential to incorporate finite size effects in terms of hard sphere repulsion is examined.

To minimize emerging numerical intricacy, the LJ potential is modified by a band limit function with a cut-off length to eliminate troublesome high frequencies in the integral

function. This process is achieved through Fourier transform to simplify and hence render the mPNP equation solvable with precision. The resultant modified NP and Poisson

equation representing electrostatic potential are then coupled to form system of equation which describes a realistic transport phenomena in ion channel. Consequently,

to discretize the 2D steady system of equations, mixed finite element approach based on Taylor hood eight node square referenced elements is adopted. In the method,

Galerkin weighted residual approach help obtain sparse matrix and finally Picard Method applied to the nonlinear terms in the algebraic equations to linearize them and

improve rate of convergence. Iterative solution for the system of equations then obtained and concentration profiles of ion species under varied steric effects for mPNP are

computed and analysed


Mathematical Model of Covid-19 Transmission Dynamics and Control Strategies

Jumanne M. Mnganga * and Naboth Sindi Zachariah

In this paper, we present a mathematical model of COVID-19 transmission dynamics and control strategies. The result reveal that the disease free equilibrium point exists and it is locally and globally asymptotically stable when the reproduction number is less than one unit and otherwise unstable when is greater than one unit. Simulation and discussions of a different variable of the model has been performed and we have compute sensitivity index of each parameter through sensitivity analysis of different embedded parameters. MATLAB of ode45 was employed perform numerical simulation analysis and the results show that there is importance of isolating infectious individual in an epidemic disease within the population.


A New One-Dimensional Finite Volume Method for Hyperbolic Conservation Laws

Jose C Pedro , Mapundi K. Banda and Precious Sibanda

In this paper, a new one-dimensional Finite Volume Method for Hyperbolic Conservation Laws is presented. The method consists in an improved numerical inter-cell flux function at the element interface. To back theoretically the method, necessary components for convergence are presented. Therefore, it is proved that the method is consistent with the P.D.E and that it is monotone with respect its variables. Moreover, to validate the approach and show its efficiency, we compute several one-dimensional test problems with discontinuous solutions and we make comparisons with traditional methods. The results show an improvement on the non-oscillatory shock-capturing properties based on the new approach.


Assessing the Impact of Age –Vaccination Structure Models on the Dynamics of Tuberculosis Transmission

Solomon T. Kwao*, Francis T. Batsa, Samuel Naandam and Gaston M. Kuzamunu

Vaccination has been the only preventive mechanism of tuberculosis (TB) yet due to inconsistencies in the efficacy of the mostly used vaccine, Baccille Calmette-Guerin (BCG), re-vaccination has been deemed to be ineffective. In this work, we sought to assess the impact of age-vaccination and re-vaccination on the transmission dynamics of TB. We developed an age-vaccination re- vaccination model to explore the disease transmission dynamics and the impact of re-vaccination on the disease transmission. By applying the vaccine within ten year intervals, we noticed that, there is no significant difference when the vaccine is administered once or many times for people less than 45 years of age. However, re-vaccination can prove to be effective when it is applied either before or immediately after the waning of the first vaccine.


Individual Preferences and the Growth Dynamics of Two Political Parties: Insights through a Simple Mathematical Model

Joseph Frank Gordon and Farai Nyabadza

Formation and the change of individual preferences from one political party to the other has now become a common trend in most democratic countries. Many party members change their preferences over political parties due to the fact that most people are not much satisfied with the trends occurring in their party’s internal democratic principles and as a result change their respective parties. This project work developed and analyzed the use of non-linear mathematical model for the spread of two political parties, the ruling party and the opposition. We used principles borrowed from infectious diseases modeling to track the changes of the membership of each political party taking into consideration preferences. The whole population was assumed to be constant and homogeneously mixed. Steady states were analytically obtained and their stability nature discussed. Conditions for the existence of single parties and the existence of both parties were obtained. Numerical simulations were also performed to support the analytical results. This study has a potential to enrich political dynamics as nations embrace democratic principles.


Matrix Representation of a Star

Mohamed Moktar Chaffar

In the present paper we define an oriented Star with imageα coefficient α 1 and we further develop the procedure for finding eigenvalues and eigenvectors for an (5 × 5) Starmatrix directly or (5 × 5) Star-matrix indirectly. we give an overview of the methods to compute matrix-multiplication of a Star image α (generally square 5 × 5) with particular emphasis on the oriented matrix.

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