Browsing by Author "Malonza, D. M."

Now showing 1 - 7 of 7
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    An optimal Control Model for Coffee Berry Disease and Coffee Leaf Rust Co-infection
    (Journal of Mathematical Analysis and Modeling, 2024) Nyaberi, H. O.; Mutuku, W. N.; Malonza, D. M.; Gachigua, G. W.; Alworah, G. O.
    In the 1980s, coffee production in Kenya peaked at an average of 1.7 million bags annually. Since then, this production has declined to the current output of below 0.9 million bags annually. Coffee berry disease (CBD) and Coffee leaf rust (CLR) are some of the causes of this decline. This is due to insufficient knowledge of optimal control strategies for CBD and CLR co-infection. In this research, we derive a system of ODEs from the mathematical model for co-infection of CBD and CLR with control strategies to perform optimal control analysis. An optimal control problem is formulated and solved using Pontryagin’s maximum principle. The outcomes of the model’s numerical simulations indicate that combining all interventions is the best strategy for slowing the spread of the CBD-CLR co-infection.
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    Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type
    (Elsevier, 2011-03-01) Malonza, D. M.; Ofoedu, E. U.
    In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.
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    The Implications of HIV treatment on the HIV-malaria coinfection dynamics: a modeling perspective
    (BioMed Central, 2015) Nyabadza, F.; Bekele, B. T.; Rúa, M. A.; Malonza, D. M.; Chiduku, N.; Kgosimore, M.
    Most hosts harbor multiple pathogens at the same time in disease epidemiology. Multiple pathogens have the potential for interaction resulting in negative impacts on host fitness or alterations in pathogen transmission dynamics. In this paper we develop a mathematical model describing the dynamics of HIV-malaria coinfection. Additionally, we extended our model to examine the role treatment (of malaria and HIV) plays in altering populations’ dynamics. Our model consists of 13 interlinked equations which allow us to explore multiple aspects of HIV-malaria transmission and treatment. We perform qualitative analysis of the model that includes positivity and boundedness of solutions. Furthermore, we evaluate the reproductive numbers corresponding to the submodels and investigate the long term behavior of the submodels. We also consider the qualitative dynamics of the full model. Sensitivity analysis is done to determine the impact of some chosen parameters on the dynamics of malaria. Finally, numerical simulations illustrate the potential impact of the treatment scenarios and confirm our analytical results
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    An improved theory of asymptotic unfoldings
    (Elsevier, 2009-08-01) Malonza, D. M.; Murdock, J.
    An asymptotic unfolding of a dynamical system near a rest point is a system with additional parameters, such that every one-parameter deformation of the original system can be embedded in the unfolding preserving all properties that can be detected by asymptotic methods. Asymptotic unfoldings are computed using normal (and hypernormal) form methods. We present a simplified and improved method of computing such unfoldings that can be used in any normal form style.
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    Normal Form for Systems with Linear Part N3(n)
    (Scientific Research, 2012-08) Gachigua, G.; Malonza, D. M.; Sigey, J.
    The concept of normal form is used to study the dynamics of non-linear systems. In this work we describe the normal form for vector fields on R3n with linear nilpotent part made up of coupled n 3x3 Jordan blocks. We use an algorithm based on the notion of transvectants from classical invariant theory known as boosting to equivariants in determining the normal form when the Stanley decomposition for the ring of invariants is known.
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    Normal Forms for Coupled Takens-Bogdanov Systems
    (Taylor & Francis, 2004) Malonza, D. M.
    The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise in normal forms for Takens-Bogdanov systems. An algorithm developed by Murdock, is then used to produce a Stanley decomposition for the (normal form module) module of the equivariants from the Stanley decomposition for the ring of invariants.
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    Stanley decomposition for coupled takens–bogdanov systems
    (Taylor & Francis, 2010-03) Malonza, D. M.
    We use an algorithm based on the notion of transvectants from classical invariant theory in determining the form of Stanley decomposition of the ring of invariants for the coupled Takens–Bogdanov systems when the Stanley decompositions of the Jordan blocks of the linear part are known at each stage. The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module.