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The Dynamics of Vector-Host Feeding Contact Rate with Saturation: A Case of Malaria in Western Kenya

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Applied Mathematics 2013年第10期4卷 1381-1391页

作者： josephine wairimu Ogana Wandera School of Mathematics University of Nairobi Nairobi Kenya

In this study, we develop an expression for a saturated mosquito feeding rate in an SIS malaria model to determine its effect on infection and transmission dynamics of malaria in the highlands of Western Kenya. The basic reproduction number is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if , the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if , there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the saturated contact rate to the basic reproduction number and the level of the endemic equilibrium are also analyzed.

关键词： SIS Host-Vector Models Malaria Contact Rate with Saturation Global Stability

Formulation of a Vector SIS Malaria Model in a Patchy Environment with Two Age Classes

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Applied Mathematics 2014年第10期5卷 1535-1545页

作者： josephine wairimu Sallet Gauthier Wandera Ogana INRIA Metz and University of Lorraine Metz France School of mathematics University of Nairobi Nairobi Kenya

We formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1- 5 years and adults, above 5 years. The susceptibility and infectivity of an individual depend on age class and residence. The large scale system with 6n equations is reduced into a compact form of 3n equations by a change of variables. Then 3n equations are vectorialized using the matrix theory to get a one dimension, compact form of the system, equation in . Using Vidyasagar theorem?[1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.

关键词： Highland Malaria Differentiated Susceptibility and Infectivity Monotone Dynamical Systems Age Structure

Mathematical Analysis of a Large Scale Vector SIS Malaria Model in a Patchy Environment

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Applied Mathematics 2014年第13期5卷 1913-1926页

作者： josephine wairimu Sallet Gauthier Wandera Ogana INRIA Metz and University of Lorraine Lorraine France School of Mathematics University of Nairobi Nairobi Kenya

We answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stability depends on the basic reproduction number, Ro?[2]. If Ro ≤1, the disease-free steady solution is globally asymptotically stable and the disease always dies out. If Ro >1, there exists a unique endemic equilibrium which is globally stable and the disease persists. Application is done on data from Western Kenya. The age structure reduces the level of infection and the populations settle to the equilibrium faster than in the model without age structure.

关键词： Highland Malaria Differentiated Susceptibility and Infectivity Monotone Dynamical Systems

Modeling Rift Valley Fever with Treatment and Trapping Control Strategies

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Applied Mathematics 2016年第6期7卷 556-568页

作者： Jonnes Lugoye josephine wairimu C. B. Alphonce Marilyn Ronoh Univeristy of Dar es Salaam Dar es Salaam Tanzania School of Mathematics University of Nairobi Nairobi Kenya

We consider a rift valley fever model with treatment in human and livestock populations and trapping in the vector (mosquito) population. The basic reproduction number R 0 is established and used to determine whether the disease dies out or is established in the three populations. When R 0 ≤ 1, the disease-free equilibrium is shown to be globally asymptotically stable and the disease does not spread and when R 0 > 1, a unique endemic equilibrium exists which is globally stable and the disease will spread. The mathematical model is analyzed analytically and numerically to obtain insight of the impact of intervention in reducing the burden of rift valley fever disease’s spread or epidemic and also to determine factors influencing the outcome of the epidemic. Sensitivity analysis for key parameters is also done.

关键词： Rift Valley Fever Mosquito Trapping Treatment Rift Valley Fever Control

A Mathematical Model of Tuberculosis with Drug Resistance Effects

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Applied Mathematics 2016年第12期7卷 1303-1316页

作者： Marilyn Ronoh Rym Jaroudi Patrick Fotso Victor Kamdoum Nancy Matendechere josephine wairimu Rose Auma Jonnes Lugoye University of Nairobi Nairobi Kenya University of Tunis El Manar Tunis Tunisia University of Dschang Yaounde Cameroon Kenyatta University Nairobi Kenya University of Dar es Salaam Dar es Salaam Tanzania

Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant tuberculosis). In this work, we extend the standard SEIRS epidemiology model of tuberculosis to include MDR-TB. For that, we considered compartments of susceptible, exposed, infected, resistant to a first line of treatment and recovered humans and we modeled the natural growth, the interactions between these populations and the effects of treatments. We calculate the basic reproduction number, , using the next generation method. The DFE and the EE are established and their stability analysis done to show that they are locally and globally asymptotically stable. Numerical analysis for the model with and without delay is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will still persist due to lack of permanent immunity to tuberculosis while the recovered can still lose their immunity to become susceptible again.

关键词： Tuberculosis Mtb MDR Reproduction Number DFE EE Stability