Research Repository :: Browsing by Author "Massawe, Estomih S."

Browsing by Author "Massawe, Estomih S."

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Computational Modelling of Cholera Bacteriophage with Treatment
(Scientific Research, 2015) Mgonja, Daniel S.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the computational modelling of cholera bacteriophage with treatment. A nonlinear mathematical model for cholera bacteriophage and treatment is formulated and analysed. The effective reproduction number of the nonlinear model system is calculated by next generation operator method. By using the next generation matrix approach, the disease-free equilibrium is found to be locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium point is not stable due to existence of forward bifurcation at threshold parameter equal to unity. Stability analysis and numerical simulations suggest that the combination of bacteriophage and treatment may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of bacteriophage virus and treatment, cholera is self-limiting in nature.
Earth Science & Climatic Change
(2015) Mwalusepo, Sizah; Massawe, Estomih S.; Affognon, H.; Okuku, Gerphas O.
The Effective Eigenvalue Method and Its Application to Stochastic Problems in Conjunction with the Nonlinear Langevin Equation
(1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
The concept of the effective eigenvalue appears to have been originally introduced into the study of relaxation problems in statistical physics by Leontovich.’ It was later developed and applied (sometimes implicitly) to a variety of stochastic problems in laser polar fluids,’ polymers,8 nematic liquid crystals? lo etc. In the present context, namely the theory of the Brownian motion, the method constitutes a truncation procedure which allows one using simple assumptions to obtain closed-form approximations to the solution of certain infinite hierarchies of differential-difference equations in the time variables. These magnetic domains, equations govern the time behavior of the statistical averages characterizing the relaxation of nonlinear stochastic systems. Thus, their solution is needed to calculate observable quantities such as the relaxation times and dynamic susceptibilities of the system
Effective-Eigenvalue Approach to the Nonlinear Langevin Equation for the Brownian motion in a Tilted Periodic Potential. II. Application to the Ring-Laser Gyroscope
(1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
The effective-eigenvalue method is used to obtain an approximate solution for the mean beat-signal spectrum for the ring-laser gyroscope in the presence of quantum noise. The accuracy of the effective-eigenvalue method is demonstrated by comparing the exact and approximate calculations. It shows clearly that the effective-eigenvalue method yields a simple and concise analytical description of the solution of the problem under consideration.
Effective-Eigenvalue Approach to the Nonlinear Langevin Equation for the Brownian motion in a Tilted Periodic Potential: Application to the Josephson Tunneling Junction
(1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.
The concept of the effective eigenvalue appears to have been originally introduced into the study of relaxation problems in statistical physics by Leontovich.’ It was later developed and applied (sometimes implicitly) to a variety of stochastic problems in laser polar fluids,’ polymers,8 nematic liquid crystals? lo etc. In the present context, namely the theory of the Brownian motion, the method constitutes a truncation procedure which allows one using simple assumptions to obtain closed-form approximations to the solution of certain infinite hierarchies of differential-difference equations in the time variables. These magnetic domains, equations govern the time behavior of the statistical averages characterizing the relaxation of nonlinear stochastic systems. Thus, their solution is needed to calculate observable quantities such as the relaxation times and dynamic susceptibilities of the system.
Evaluation of Continuous Host-Parasitoid Models
(Academic Journals, 2011-03) Mwalusepo, Siza; Tonnang, Henri E. Z.; Massawe, Estomih S.
In this paper the performance of continuous host-parasitoid models were investigated. The parameter values for several well-known models: Lotka-volterra, Holling Tanner Type 2, Holling Tanner Type 3, Leslie, Bazykin, Beddington-DeAngelis, Yodzis and Rosenzwing-Macarthur models were estimated. The models were tested on 40 consecutive sets of time series data collected at 14 days interval for pest and parasitoid population obtained from a highland cabbage growing area in Eastern Kenya. Model parameters were estimated from the minimization of the loss functions between the theoretical and experimental time series datasets following the Nelder-Mead multidimensional method. Initial values of population size and parameters were randomly chosen. Durbin-Watson statistic was applied for comparison of model outputs and experimental population trajectories. Among the eight different hostparasitoid models, Holling Tanner model Type 3 presented relatively better approximations compared to the other models.
Exact Analytic Formula for the Correlation Time of a Single-Domain Ferromagnetic Particle
(1994) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single-domain ferromagnetic particle are presented for the simple uniaxial potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130, 1677 (1963)]. This is accomplished by expanding the spatial part of the distribution function of magnetic-moment orientations on the unit sphere in the Fokker-Planck equation in Legendre polynomials. This leads to the three-term recurrence relation for the Laplace transform of the decay functions. The recurrence relation may be solved exactly in terms of continued fractions. The zero-frequency limit of the solution yields an analytic formula for T∥ as a series of confluent hypergeometric (Kummer) functions which is easily tabulated for all potential-barrier heights. The asymptotic formula for T∥ of Brown is recovered in the limit of high barriers. On conversion of the exact solution for T∥ to integral form, it is shown using the method of steepest descents that an asymptotic correction to Brown’s high-barrier result is necessary. The inadequacy of the effective-eigenvalue method as applied to the calculation of T∥ is discussed.
Exact Analytic Formula for the Correlation Times for Single Domain Ferromagnetic Particles.
(Elsevier, 1993) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single domain ferromagnetic particle are presented for the simple uniaxial (Maier-Saupe) potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130 (1963) 1677].
Exact Solution for the Correlation Times of Dielectric Relaxation of a Single Axis Rotator with Two Equivalent Sites
(1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
It is shown how exact formulas for the longitudinal and transverse dielectric correlation times and complex polar&ability tensor, of a single axis rotator with two equivalent sites may be found. This is accomplished by writing the Laplace transforms of the dipole autocorrelation functions as three term recurrence relations and solving them in terms of continued fractions. The solution of these recurrence relations, in the zero frequency limit, yields the correlation times in terms of modified Bessel functions of the first kind. The previous result of Lauritzen and Zwanzig for the longitudinal relaxation time, based on an asymptotic expansion of the SturmLiouville equation, is regained in the limit of high potential barriers.
Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants
(Scientific Research, 2015-01) Ainea, Neterindwa; Massawe, Estomih S.; Makinde, Oluwole D.; Namkinga, Lucy
In this paper, we derive and analyse rigorously a mathematical model of control strategies (screening, education, health care and immunization) of HCV in a community with inflow of infected immigrants. Both qualitative and quantitative analysis of the model is performed with respect to stability of the disease free and endemic equilibria. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV model in a community with inflow of infected immigrants. However, analysis shows that screening, education, health care and immunization have the effect of reducing the transmission of the disease in the community.
Modeling Laminar Flow between a Fixed Impermeable Disk and a Porous Rotating Disk
(Academic Journals, 2009) Kavenuke, D. P.; Massawe, Estomih S.; Makinde, Oluwole D.
We formulate a mathematical model that governs operations of many engineering systems particularly the ceiling fan to explain the fluid flow between the fixed impermeable and the porous rotating disks. The model is based on the continuity and the Navier-Stokes equations which are reduced into a set of coupled ordinary differential equations through transformation by similarity variables. The coupled ordinary differential equations are solved using perturbation techniques and the series solution obtained is improved by Paté’s approximation. Our results meet the supposition that, with laminar flow regime, suction increases with increasing speed of rotation of the rotating porous disk and these are shown on the graphical representations.
Modelling the Effect of Screening on the Spread of HIV Infection in a Population with Variable Inflow of Infective Immigrants
(Scientific Research, 2011) Shabani, Issa; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the combined effects of screening and variable inflow of infective immigrants on the spread of HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) in a population of varying size. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. The results show that the reproductive number R0 >1 as the rate of inflow of infective immigrants increases leading to persistence of the disease in the population. However, the presence of screening greatly reduces the spread of HIV/AIDS. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.
Modelling the Effect of Treatment and Infected Immigrants on the Spread of Hepatitis C Virus Disease with Acute and Chronic Stages
(2012) Ainea, Neterindwa; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus (HCV) disease with Acute and Chronic stages. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However the disease becomes more endemic due to the presence of infected immigrants in the community. It is also shown that in the presence of treatment, the rate of infected immigrants (acute and chronic) decreases and consequently the treated in-fected individuals decreases continuously. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and infected immigrants on the spread of the disease with acute and chronic stages.
Modelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infection
(Scientific Research, 2015) Kimaro, Magreth A.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.
Modelling the Pyrolysis and Combustion of Wood
(2012) Massawe, Estomih S.; Salim, Said S.; Makinde, Oluwole D.
This paper examines the chemical kinetics of cellulosic material with fixed and varying temperatures. The combustion kinetics of wood together with Arrhenius equation is used in derivation of the model. The governing nonlinear ordinary differential equations with initial conditions are solved numerically. The results obtained are presented graphically for the purpose of showing the pyrolysis and combustion of wood and impact of wood burning for both fixed and varying temperatures. It is observed that charcoal and gases yields are the end products formed during the processes. However it is observed that gases are highly produced at varying temperatures. However for both fixed and varying temperatures, the decomposition reaction of wood (cellulose) in the system leads to the separation of the components of wood giving charcoal and gases as end products, but the gases are highly produced at moderate temperatures.
Predicting the Impact of Temperature Change on the Future Distribution of Maize Stem Borers and Their Natural Enemies along East African Mountain Gradients Using Phenology Models
(2015) Mwalusepo, Sizah; Tonnang, Henri E. Z.; Massawe, Estomih S.; Okuku, Gerphas O.; Khadioli, Nancy; Johansson, Tino; Calatayud, P. A.; Le Ru, Bruno P.
Lepidopteran stem borers are among the most important pests of maize in East Africa. The objective of the present study was to predict the impact of temperature change on the distribution and abundance of the crambid Chilo partellus, the noctuid Busseola fusca, and their larval parasitoids Cotesia flavipes and Cotesia sesamiae at local scale along Kilimanjaro and Taita Hills gradients in Tanzania and Kenya, respectively. Temperature-dependent phenology models of pests and parasitoids were used in a geographic information system for mapping. The three risk indices namely establishment, generation, and activity indices were computed using current temperature data record from local weather stations and future (i.e., 2055) climatic condition based on downscaled climate change data from the AFRICLIM database. The calculations were carried out using index interpolator, a sub-module of the Insect Life Cycle Modeling (ILCYM) software. Thin plate algorithm was used for interpolation of the indices. Our study confirmed that temperature was a key factor explaining the distribution of stem borers and their natural enemies but other climatic factors and factors related to the top-down regulation of pests by parasitoids (host-parasitoid synchrony) also played a role. Results based on temperature only indicated a worsening of stem borer impact on maize production along the two East African mountain gradients studied. This was attributed to three main changes occurring simultaneously: (1) range expansion of the lowland species C. partellus in areas above 1200 m.a.s.l.; (2) increase of the number of pest generations across all altitudes, thus by 2055 damage by both pests will increase in the most productive maize zones of both transects; (3) disruption of the geographical distribution of pests and their larval parasitoids will cause an improvement of biological control at altitude below 1200 m.a.s.l. and a deterioration above 1200 m.a.s.l. The predicted increase in pest activity will significantly increase maize yield losses in all agro-ecological zones across both transects but to a much greater extent in lower areas.
Smallholder Farmers' Perspectives on Climatic Variability and Adaptation Strategies in East Africa: The Case of Mount Kilimanjaro in Tanzania, Taita and Machakos Hills in Kenya
(2015) Mwalusepo, Sizah; Massawe, Estomih S.; Affognon, H.; Okuku, G.; Kingori, Sarah; Mburu, Peter D. M.; Ong’amo, Georges; Muchugu, Eric; Calatayud, P. A.; Landmann, Tobias; Muli, Eliud; Raina, Suresh K.; Johansson, Tino; Le Ru, Bruno P.
Climate change is expected to have serious economic and social impacts in East Africa, particularly on rural farmers whose livelihoods largely depend on rain-fed agriculture, hence adaptation is required to offset projected drawbacks of climate change on crop productivity. This paper examines farmers' perceptions and understanding of climatic variability, coping strategies adopted and factors that influence the choice of a particular adaptation. The study uses cross section data collected from 510 farmers in three mountain gradients sites, namely; Mount Kilimanjaro of Tanzania, Taita and Machakos Hills of Kenya. Farmers’ perceptions were compared to actual trend in meteorological records over the last thirty years (1981-2010). The result revealed that farmers in East Africa were partly aware of climate variability, mainly in temperature and rainfall patterns. Many respondents reported that conditions are drier and rainfall timing is becoming less predictable. The perception of farmers on temperature and rainfall were in line with recorded meteorological data, but contrary with that of recorded rainfall in Machakos which was perceived to be decreasing by the farmers. Farmers perceived changes in rainfall and temperature to have negative effects on the production and management of crops. The common adaptation strategies used by farmers include water harvesting, soil conservation techniques and shifting of planting periods. The most important variables affecting farmers choices in regards to adaptation option were, lack of access to credit, farming experience and household size. As a conclusion, there is a need for these factors to be taken into account in the development and implementation of smallholder farmers’ adaptation strategies to climate variability in East Africa. Additionally, dedicated capacity building and extensive outreach initiatives on adaptation through governments, researchers, policy-makers and the farmers groups themselves are needed to achieve large scale success.
Spatially Continuous Dataset at Local Scale of Taita Hills in Kenya and Mount Kilimanjaro in Tanzania
(Elsevier, 2016) Mwalusepo, Sizah; Massawe, Estomih S.; Johansson, Tino
Climate change is a global concern, requiring local scale spatially continuous dataset and modeling of meteorological variables. This dataset article provided the interpolated temperature, rainfall and relative humidity dataset at local scale along Taita Hills and Mount Kilimanjaro altitudinal gradients in Kenya and Tanzania, respectively. The temperature and relative humidity were recorded hourly using automatic onset THHOBO data loggers and rainfall was recorded daily using GENERALR wireless rain gauges. Thin plate spline (TPS) was used to interpolate, with the degree of data smoothing determined by minimizing the generalized cross validation. The dataset provide information on the status of the current climatic conditions along the two mountainous altitudinal gradients in Kenya and Tanzania. The dataset will, thus, enhance future research.
Stability Analysis of Competing Insect Species for a Single Resource
(Hindawi Publishing Corporation, 2014) Mwalusepo, Sizah; Tonnang, Henri E. Z.; Massawe, Estomih S.; Johansson, Tino; Le Ru, Bruno P.
The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.
Temporal Model for Dengue Disease with Treatment
(Scientific Research, 2015) Massawe, Laurencia N.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the effect of treatment of Dengue fever disease. A non linear mathematical model for the problem is proposed and analysed quantitatively using the stability theory of the differential equations. The results show that the disease-free equilibrium point is locally andglobally asymptotically stable if the reproduction number (R ) 0 is less than unity. The additive compound matrices approach is used to show that the dengue fever model’s endemic equilibrium point is locally asymptotically stable when trace, determinant and determinant of second additive compound matrix of the Jacobian matrix are all negative. However, treatment will have a control of dengue fever disease. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the dengue fever disease with treatment.

Browsing by Author "Massawe, Estomih S."

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