Applied Mathematics
Permanent URI for this community
Applied Mathematics
Browse
Browsing Applied Mathematics by Title
Now showing 1 - 7 of 7
Results Per Page
Sort Options
- ItemAn Analysis of Eccentricity-Based Invariants for Biochemical Hypernetworks(Wiley, 2021-10-06) Rashid, M.A.; Ahmad, S.; Siddiqui, M.K.; Manzoor, S.; Dhlamini, M.Biological proceedings are well characterized by solid illustrations for communication networks. The framework of biological networks has to be considered together with the expansion of infectious diseases like coronavirus. Also, the graph entropies have established themselves as the information theoretic measure to evaluate the architectural information of biological networks. In this article, we examined conclusive biochemical networks like t‐level hypertrees along with the corona product of hypertrees with path. We computed eccentricity‐based indices for the depiction of aforementioned theoretical frameworks of biochemical networks. Furthermore, explicit depiction of the graph entropies with these indices is also measured.
- ItemCombined Optimal Stopping and Mixed Regular-Singular Control of Jump Diffusions(Scientific Research Publishing, 2021-04-01) Kusaya, C.; Mandiudza, M.; Mwareya, N.; Matete, C.; Shambira, L.; Ngaza, N.In this paper, we examine a model that maximises dividend payments for an insurance company with a debt liability. We assume that the company has a policy to reinvest a proportion of its surplus cash before paying dividends to shareholders. We model the dynamics of the cash reserves as a jump-diffusion process. Combined optimal stopping and mixed regular-singular control of the jump-diffusion process is presented and investigated. In the paper, we show that when the premium rate is less than the liability rate , then the company should not get into business and the optimal dividend policy is to immediately pay out the initial cash reserve as dividends to shareholders. For the case , we show that the optimal risk management depends on the current level of the cash reserves. We demonstrate that the company’s optimal dividend policy is to pay out as dividends surplus cash above a predetermined threshold. We also present numerical examples to illustrate the results obtained.
- ItemModelling and analysis of Limnothrissa Miodon population in Lake Kariba with harvesting predation and environmental factors(2022) Mutasa, F.K.Limnothrissa miodon, called kapenta locally, is a natural resource which provides Zimbabwean and Zambian communities with protein and is a source of livelihoods to fisherman, wholesalers and retailers. The kapenta catches from the Lake Kariba fishery have been declining and it has been attributed to harvesting, climate change, predation and reduced nutrient inflow into the lake. Studies have been done using regression, surplus production models and analytical models. No studies have been done involving a nutrient, plankton, kapenta and tigerfish food chain as a dynamical system. The aim of this research is to formulate a deterministic, non-linear model of ordinary differential equations and analyse the impact of nutrients, harvesting, predation and lake surface water temperature on the population density of kapenta. Mathematical preliminaries such as positivity and existence of solutions are done. Local and global stability analysis of equilibrium points are done using the Routh-Hurwitz criterion and Lyapunov method respectively. Numerical simulations are done using Runge-Kutta method of order 4 in MATLAB and Wolfram Mathematica. Results show that nutrients are key to the productivity of the water body and kapenta will continue to thrive as long as the nutrient inflow rate is greater than some threshold value. Results also show that the coexistence equilibrium is stable provided certain conditions are satisfied and globally unstable when feasible. A maximum sustainable yearly catch of 34668.59 tonnes is obtained and is within the range obtained by other authors. Optimal control theory applied to a kapenta model with harvesting shows that not more than 505 fishing units to be licensed to operate on Lake Kariba, with 278 on the Zimbabwean side and 227 on the Zambian side and currently there is overcapacity in the lake. Bifurcation analysis of the kapenta model with tigerfish predation shows existence of an Poincar ́e-Androv-Hopf bifurcation with a possibility of chaos for the zooplankton growth rate parameter. Bifurcation type, point, existence, angular frequency, period, stability and direction are determined for some model control parameters. Lyapunov exponents are used for determining stability of periodic orbits and to check for possibility of chaos. Simulation results show that predator-prey dynamics of tigerfish and kapenta show oscillatory behaviour which is ecologically stable and agrees with actual data and therefore reflects reality. Lake surface water temperature was added as an environmental factor to the kapenta model with harvesting and predation. Numerical results show that the population density of kapenta declines after a lake surface water temperature of 30◦C. Warming of the lake has a negative effect on the more palatable Chlorophyceae and this results in a decrease in the density of kapenta in Lake Kariba.
- ItemNumerical Analysis of Couple Stress Nanofluid in Temperature Dependent Viscosity and Thermal Conductivity(Springer Nature, 2021-02-24) Dhlamini, M.; Mondal, H.; Sibanda, P.; Motsa, S.This communication reports on an innovative study of two-dimensional couple stress fluid 3 with effect of viscosity and conductivity. We proposed a new model based on temperature dependent variable thermal conductivity on kinetic theory. Our model assumes that thermal conductivity is a decreasing function of temperature rather than an increasing function. The effect of the three key parameters, viscosity, thermal conductivity and couple stress parameter are analyzed. The coupled non-linear system is further validated numerically using the spectral quasilinearization method. The method is found to be accurate and convergent. Increasing the temperature dependent parameter for viscosity is shown to reduce the heat mass transfer rates at the surface. Increasing thermal conductivity and the couple stress parameter increased the heat mass transfer rates on the boundary surface.
- ItemOn Degree-Based Topological Indices for Strong Double Graphs(Hindawi, 2021-02-02) Rafiullah, M.; Siddiqui, H.M.A.; Siddiqui, M.K.; Dhlamini, M.A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.
- ItemOn the Dynamics of a Fractional-Order Ebola EpidemicModel with Nonlinear Incidence Rates(Wiley Online Library, 2021-12-03) Chinyoka, M.; Gashirai, T. B.; Mushayabasa, S.We propose a new fractional‐order model to investigate the transmission and spread of Ebola virus disease. The proposed model incorporates relevant biological factors that characterize Ebola transmission during an outbreak. In particular, we have assumed that susceptible individuals are capable of contracting the infection from a deceased Ebola patient due to traditional beliefs and customs practiced in many African countries where frequent outbreaks of the disease are recorded. We conducted both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Model parameters were estimated based on the 2014‐2015 Ebola outbreak in Sierra Leone. In addition, numerical simulation results are presented to demonstrate the analytical findings.
- ItemOn Topological Analysis of Entropy Measures for Silicon Carbides Networks(Wiley, 2021-11-05) Wang, X.L.; Siddiqui, M.K.; Kirmani, S.A.K.; Manzoor, S.; Ahmad, S.; Dhlamini, M.The silicon material has provoked and stimulated significant research concern to a considerable extent taking into account its marvelous mechanical, optical, and electronic properties. Naturally, silicons are semiconductors and are utilized in the formation of various materials. For example, it is used in assembling the electronic based gadgets. In this article, we have studied the 2D structure of silicon carbide Si2C3 − I[m, n] and Si2C3 − II[m, n] and then continued to discuss some degree grounded topological descriptors in association with their corresponding entropy measures. We extend this computation to the quantitative and pictorial comparisons which could be beneficial in the structure amendment for effective implementation.