Computational and Communication Science Engineeringhttps://dspace.nm-aist.ac.tz/handle/20.500.12479/42024-03-28T18:27:41Z2024-03-28T18:27:41ZModeling transmission dynamics and control of anthraxEfraim, Joely Ehttps://dspace.nm-aist.ac.tz/handle/20.500.12479/24832024-03-07T00:00:28Z2019-03-01T00:00:00ZModeling transmission dynamics and control of anthrax
Efraim, Joely E
Anthrax is a zoonotic disease caused by Bacillus anthraces. In this study the deterministic
mathematical models for transmission dynamics of anthrax in absence and presence of control
strategies in humans and animals are presented and analyzed to determine which parameters
are sensitive to the disease and how will control strategies help to eradicate the disease. Using
normalized sensitivity index, sensitivity index of each parameter with respect to basic repro-
duction number R0 is derived and find that, parameters such as anthrax transmission’s rate β ,
animal’s recruitment rate ba, animal’s natural death rate, and pathogen’s natural death rate are
most sensitive to the transmission dynamics of anthrax. Stability analysis for equilibrium states
by linearization, Metzler matrix, and Lyapunov function shows that the disease-free equilibrium
is locally and globally asymptotically stable when R0 < 1 and endemic equilibrium is globally
asymptotically stable when R0 > 1. The analysis shows that when free pathogens are destroyed
with fumigants both susceptible humans and animals flourish while infected humans and an-
imals decrease. It is also found that pathogens and carcasses decrease due to the fumigation
effect. The analysis also shows that when carcasses are incinerated and removed from the af-
fected area both humans and animals increase while infected humans and animals decrease. The
analysis also shows that incineration and complete removal of carcasses makes the population
of carcasses and pathogens decrease. The study also found that when all control strategies such
as fumigation, incineration and complete removal of carcasses, animal’s treatment, and humans
treatment are all administered both susceptible humans and animals increase, infected humans
and animals decrease and carcasses and pathogens decrease.
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Master’s in Mathematical and Computer Sciences and Engineering of the Nelson
Mandela African Institution of Science and Technology
2019-03-01T00:00:00ZSuitability of Vermiculite and Rice Husk Ash as Raw Materials for Production of Ceramic TilesAbeid, SaidPark, Seungyonghttps://dspace.nm-aist.ac.tz/handle/20.500.12479/24732024-02-29T00:00:33Z2018-02-03T00:00:00ZSuitability of Vermiculite and Rice Husk Ash as Raw Materials for Production of Ceramic Tiles
Abeid, Said; Park, Seungyong
The challenging issues in ceramic tiles are low mechanical strength, thermal discomfort and high production costs. And in most efforts to improve strength, emphasis has been placed on minimization of quartz content in the ceramic tiles formula. This is due to β-α phase inversion of quartz which occurs at 573°C during cooling resulting to the development of stresses which initiate fracture and affects the strength of the final body. The objective of this work was to evaluate the possibility of using vermiculite and rice husk ash (RHA) in the composition of ceramic tile body. Initially, a typical ceramic body composed of the mixture of vermiculite and RHA batched with clay, feldspar, quartz and kaolin was prepared. Ceramic bodies were then obtained from this ceramic mixture by pressing samples at a forming pressure of 35MPa. These bodies were then fired at 1180°C in a laboratory furnace and finally the changes in the physical and mechanical properties caused by the introduction of vermiculite and RHA were tested and evaluated. The chemical composition of the raw samples was analyzed by X-ray fluorescence (XRF) while the phase composition was investigated using X-ray diffraction (XRD). The morphology of the powdered samples was studied by using Scanning electron microscopy (SEM). The bulk density and open porosity of the sintered ceramic bodies were evaluated using Archimedes ‘principle while the flexural rupture strength was determined by the three point bending test method. The major chemical compounds in vermiculite raw sample were SiO2, Al2O3 and Fe2O3 while RHA sample was found to contain mainly SiO2. From the XRD analysis, vermiculite sample had crystalline vermiculite while RHA sample had amorphous silica at low temperature below 900°C and crystallized (tridymite) above 900°C. The results from physical and mechanical properties tests show that with addition of vermiculite and RHA, the percentage of porosity, water absorption and linear shrinkage were increasing while the bulk density and bending strength of the fired ceramic bodies decreased. Among the studied compositions tile bodies made from a blend containing 20% wt. vermiculite and 5% wt. RHA were found to have the best properties for ceramic tiles applications. For this combination the percentage of porosity, water absorption and linear shrinkage were 12.08%, 7.60% and 3.29% while the bulk density and bending strength were 1.88 g/cm3 and 18.84 MPa respectively. These values were close to the required standards of wall and floor tiles.
This research article was published in the International Journal of Materials Science and Applications, Volume 7, Issue 2, 2018
2018-02-03T00:00:00ZModeling the dynamics and control of cassava mosaic diseaseMagoyo, Florencehttps://dspace.nm-aist.ac.tz/handle/20.500.12479/24722024-02-29T00:00:32Z2019-03-01T00:00:00ZModeling the dynamics and control of cassava mosaic disease
Magoyo, Florence
Cassava mosaic disease (CMD) is caused by cassava mosaic virus (CMV) and is transmitted by
the whitefly vector called Bemisia tabaci. In this study, the deterministic model for transmission
dynamics of CMD is formulated by considering the whitefly vector, cassava resistant and sus-
ceptible breeds, and infected cassava. The basic reproduction number R0 and sensitivity index
for each parameter with respect to basic reproduction number R0 are computed to determine
which parameters are sensitive to the dynamics of cassava mosaic disease. Analysis shows that
the death rate of whitefly vectors, infection rate for susceptible vectors, the number of vectors
that can be supported and recruitment rate of whitefly are most sensitive parameters to the dy-
namics of cassava mosaic disease. The disease stability at cassava mosaic free equilibrium was
investigated by using metzler matrix (box invariance). We found that disease free equilibrium is
asymptotically stable when R0 < 1. By using Lyapunovs direct method and LaSalles invariant
principle, endemic equilibrium is asymptotically stable when R0 > 1. Numerical simulation in-
dicates that, cassava new infections increase as many whitefly vectors are recruited and acquire
cassava mosaic disease. When controls are not considered, the susceptible breed and cassava
resistant breed will be wiped out after five and ten months respectively. To control the disease
interventions which target whitefly vectors, farmers are encouraged to apply control strategies
such as spraying of insecticide, using of vector-resistant varieties, phytosanitation which in-
volves the removal of infected cassava plants from the farm, crop hygiene and the use of free
stem cutting method. Analysis shows that spraying of insecticide and the death of whitefly vec-
tor plays the most important role in the eradication of CMD. This study concludes that, spraying
of insecticide is the possible way to get rid of both infected and susceptible vector as well as the
removal of infected cassava plants from the farm will help to reduce the contact rate between
plants and vectors.
A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of
Master’s in Mathematical and Computer Sciences and Engineering of the Nelson
Mandela African Institution of Science and Technology
2019-03-01T00:00:00ZModelling optimal control of harvested prey predator system incorporating a prey refugeCharles, Mfanohttps://dspace.nm-aist.ac.tz/handle/20.500.12479/24692024-02-29T00:00:30Z2019-03-01T00:00:00ZModelling optimal control of harvested prey predator system incorporating a prey refuge
Charles, Mfano
prey-predator interactions have been an important role in the dynamics of species populations.
This work presents mathematical model for Modelling Optimal control of Harvested prey-
predator system incorporating a prey refuge using deterministic differential equations. This
study, develops two harvested prey-predator species, in which both species are affected by
over-harvesting, furthermore the predator is affected by prey refuge. The intention is to in-
vestigate the impacts of over-harvesting to prey-predator species and suggest control strategies
to alleviate the problem of loss of prey-predator species. The analysis of stability of equilib-
rium points were done by Jacobian matrix, Global stability analysis is done using Lyapunov
function while the analysis of optimal control was done using Pontrygians maximum principle
(PMP) and Hamiltonian principle. The control strategy suggested is the creation of reserve ar-
eas with restrictions of harvesting. The results obtained from theoretical and numerical analysis
of the prey-predator with harvesting without control strategies showed that, harvesting affect the
prey-predator species negatively. However, the results obtained from numerical analysis of the
prey-predator model with control strategies showed that, the use of control strategy encourage
the survival of both species
A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of
Master’s in Mathematical and Computer Sciences and Engineering of the Nelson
Mandela African Institution of Science and Technology
2019-03-01T00:00:00Z