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Shirley Abelman [3]S. Abelman [3]
  1.  19
    Gas Exchange Models for a Flexible Insect Tracheal System.S. M. Simelane, S. Abelman & F. D. Duncan - 2016 - Acta Biotheoretica 64 (2):161-196.
    In this paper two models for movement of respiratory gases in the insect trachea are presented. One model considers the tracheal system as a single flexible compartment while the other model considers the trachea as a single flexible compartment with gas exchange. This work represents an extension of Ben-Tal’s work on compartmental gas exchange in human lungs and is applied to the insect tracheal system. The purpose of the work is to study nonlinear phenomena seen in the insect respiratory system. (...)
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  2.  13
    A Mathematical Model for the Transmission Dynamics of Lymphatic Filariasis with Intervention Strategies.S. M. Simelane, P. M. Mwamtobe, S. Abelman & J. M. Tchuenche - 2019 - Acta Biotheoretica 68 (3):297-320.
    This manuscript considers the transmission dynamics of lymphatic filariasis with some intervention strategies in place. Unlike previously developed models, our model takes into account both the exposed and infected classes in both the human and mosquito populations, respectively. We also consider vaccinated, treated and recovered humans in the presented model. The global dynamics of the proposed model are completely determined by the basic and effective reproduction numbers. We then use Lyapunov function theory to find the sufficient conditions for global stability (...)
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  3.  13
    Microscale Gaseous Slip Flow in the Insect Trachea and Tracheoles.F. D. Duncan, S. Abelman & S. M. Simelane - 2017 - Acta Biotheoretica 65 (3):211-231.
    An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier–Stokes equations with a slip boundary condition are (...)
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  4.  10
    A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding.Jean M. Tchuenche, Shirley Abelman & Solomon Kadaleka - 2021 - Acta Biotheoretica 69 (4):511-541.
    To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0<1$$\end{document}, while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published (...)
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  5.  14
    A Mathematical Model of the Transmission Dynamics of Bovine Schistosomiasis with Contaminated Environment.Jean M. Tchuenche, Shirley Abelman & Solomon Kadaleka - 2022 - Acta Biotheoretica 70 (1):1-28.
    Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is computed and used to investigate the local stability of the model’s steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable Lyapunov function. (...)
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  6.  15
    The Role of Hyalomma Truncatum on the Dynamics of Rift Valley Fever: Insights from a Mathematical Epidemic Model.Henri E. Z. Tonnang, Shirley Abelman & Sansao A. Pedro - 2016 - Acta Biotheoretica 65 (1):1-36.
    To date, our knowledge of Rift Valley fever disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit (...)
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