Applied Mathematics Publications
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- ItemStability Analysis and Optimal Control of a Limnothrissa Miodon Model with Harvesting(Discrete Dynamics in Nature and Society, 2022-05-05) Mutasa, F.K.; Jones, B.; Hove-Musekwa, S.D.; Tendaupenyu, I.H.; Nhiwatiwa, T.; Ndebele-Murisa, M.R.We construct a theoretical, deterministic mathematical model of the dynamics of Limnothrissa miodon with nutrients, phytoplankton, and zooplankton and investigate the effect of harvesting on the population density of Limnothrissa miodon in a lake. For the autonomous model, results from local stability analysis are in agreement with numerical simulations in that the coexistence equilibrium is locally stable, provided certain conditions are satisfied. The coexistence equilibrium is globally unstable if it is feasible. Numerical results show that a stable limit cycle exists for the nonautonomous model. Optimal control results show an optimal harvesting monthly effort of 15394 boat nights which corresponds to 505 fishing units, showing that there is overcapacity in Lake Kariba. A maximum sustainable annual catch of 34669 tonnes is obtained and simulation results show that Limnothrissa miodon abundance is more closely related to nutrient inflow than to harvesting.
- ItemA mathematical model for bioconvection flow with activation energy for chemical reaction and microbial activity(Indian Academy of Sciences, 2022-01-23) Dhlamini, M.; Mondal, H.; Sibanda, P.; Mosta, S.S.; Shaw, S.In most of the industrial processes, it is of paramount importance to control the heat and mass transfer rates to ensure high-quality products. Using nanofluids instead of ordinary fluids and using motile micro-organisms are some of the techniques to control heat and mass transfer rates. In some recent studies of bioconvection flow, activation energy, Brownian motion and thermophoretic effects are considered only for the solute and not for the microbes. Our current study incorporates these effects for the motile micro-organisms too. Few, if any results of this nature exist in literature. A system of partial differential equations is formulated to incorporate the effects of these parameters. The system of equations are solved numerically using the spectral quasi-linearisation method to gain an insight into the influence of key parameters on the fluid and flow properties. The thermophoretic force, the Brownian motion and activation energy are significant contributors in the microbes’ dynamics. The concentration of microbes decreases with an increase in the thermophoretic force and increases with increasing microbe’s Brownian motion parameter. Based on our results, we conclude that increasing activation energy leads to a decrease in microbes’ velocity. The inclusion of the microbes’ Brownian motion proved to be significant as this was shown to have an impact on the temperature, solute concentration and microbes’ concentration in the boundary layer.
- 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.
- 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.