Bio

Research intrests

Mathematical modeling of emerging infectious diseases with delay, Ebola.
Modeling insecticides resistance in vectors and drug resistance in human.

My research interests include:

Mathematical modeling of emerging infectious diseases with delay, Ebola.
Modeling insecticides resistance in vectors and drug resistance in human.

Publications


2020

Ronoh, M, Chirove F, Wairimu J, Ogana W.  2020.  Evidence-based modeling of combination control on Kenyan youth HIV/AIDS dynamics. PloS one. 15(11):0242491. AbstractWebsite

We formulate a sex-structured deterministic model to study the effects of varying HIV testing rates, condom use rates and ART adherence rates among Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and Young Men (ABYM) populations in Kenya. Attitudes influencing the Kenyan youth HIV/AIDS control measures both positively and negatively were considered. Using the 2012 Kenya AIDS Indicator Survey (KAIS) microdata we constructed our model, which we fitted to the UNAIDS-Kenya youth prevalence estimates to understand factors influencing Kenyan youth HIV/AIDS prevalence trends. While highly efficacious combination control approach significantly reduces HIV/AIDS prevalence rates among the youth, the disease remains endemic provided infected unaware sexual interactions persist. Disproportional gender-wise attitudes towards HIV/AIDS control measures play a key role in reducing the Kenyan youth HIV/AIDS prevalence trends. The female youth HIV/AIDS prevalence trend seems to be directly linked to increased male infectivity with decreased female infectivity while the male youth prevalence trend seems to be directly associated with increased female infectivity and reduced male infectivity.

Calistus N Ngonghala, Wairimu J, Jesse Adamski, Desai H.  2020.  IMPACT OF ADAPTIVE MOSQUITO BEHAVIOR AND INSECTICIDE-TREATED NETS ON MALARIA PREVALENCE. Journal of Biological Systems. 28(2):515-542. AbstractWebsite

Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year.1 Most of these cases and deaths are among children under five. The main control method in malaria endemic regions has been through the use of insecticide-treated nets (ITNs). Although this approach has been fairly successful, the gains are threatened by mosquito-resistance to pyrethroids (insecticides on nets), physical and chemical degradation of ITNs that reduce their efficacy, inconsistent and improper use by humans, etc. We present a model to investigate the effects of ITN use and mosquito-resistance and adaptation to pyrethroids used to treat bed nets on malaria prevalence and control in malaria endemic regions. The model captures the development and loss of resistance to insecticides, the effects of ITN use on malaria control in a setting where proper and consistent use is not …

Ronoh, M, Chirove F, Wairimu J, Ogana W.  2020.  MODELING DISPROPORTIONAL EFFECTS OF EDUCATING INFECTED KENYAN YOUTH ON HIV/AIDS. Journal of Biological Systems. 28(2):311-349. AbstractWebsite

We formulate an age and sex-structured deterministic model to assess the effect of increasing comprehensive knowledge of HIV/AIDS disease in the infected Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and Young Men (ABYM) populations in Kenya. Mathematical analysis of infection through sub-network analysis was carried out to trace various infection routes and the veracity of various transmission routes as well as the associated probabilities. Using HIV data in Kenya on our model, disproportional effects were observed when dispensation of comprehensive knowledge of HIV/AIDS was preferred in one population over the other. Effective dispensation of comprehensive knowledge of HIV/AIDS in both the infected AGYW and ABYM populations significantly slows down the infection spread but may not eradicate it.

2018

Wairimu, J, Chirove F, Ronoh M, Malonza DM.  2018.  Modeling the effects of insecticides resistance on malaria vector control in endemic regions of Kenya. Elsevier. Volume 174:49-59. AbstractWebsite

We present a model to investigate the effects of vector resistance to control strategies. The model captures the development of resistance as well as loss of resistance in mosquitoes and how these affect the progress in malaria control. Important thresholds were calculated from mathematical analysis and numerical results presented. Mathematical results reveal the existence of the disease free and endemic equilibria whose existence and stability depends on the control reproduction number, R c. The disease persist when the R c> 1 and dies out when R c< 1. Control strategies use and adherence needs to be highly efficacious to thwart the effects of insecticides resistance. Moreover, it is not enough to just eradicate resistant mosquitoes

2016

Jonnes Lugoye, Wairimu J, CB Alphonce, Ronoh M.  2016.  Modeling Rift Valley fever with treatment and trapping control strategies. Scientific Research Publishing. 7(6):556. AbstractWebsite

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.

Wairimu, J, Ronoh M.  2016.  Modeling Insecticide Resistance in Endemic Regions of Kenya. Scientific Research Publishing. 7(6):542. AbstractWebsite

In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number R 0 is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if R 0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if R 0 > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduction number and to the level of the endemic equilibrium is analyzed.

Ronoh, M, Rym Jaroudi, Patrick Fotso, Victor Kamdoum, Nancy Matendechere, Wairimu J, Rose Auma JL.  2016.  A Mathematical Model of Tuberculosis with Drug Resistance Effects. https://www.scirp.org/journal/paperinformation.aspx?paperid=68984. 7(12):1303-1316. AbstractWebsite

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

2014

Wairimu, J, Sallet G, Ogana W.  2014.  Formulation of a vector SIS malaria model in a patchy environment with two age classes. Scientific Research Publishing. 5(10):1535-1545. AbstractWebsite

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 susceptibili-ty 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 n 3  . 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 circula-tion of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for the n-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.

Wairimu, J, Sallet G, Ogana W.  2014.  Mathematical analysis of a large scale vector SIS malaria model in a patchy environment. Scientific Research Publishing. 5(13):1913-1926. AbstractWebsite

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, 0  [2]. If 0 1  ≤ , the dis-ease-free steady solution is globally asymptotically stable and the disease always dies out. If 0 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.

2013

Wairimu, J, Wandera O.  2013.  The Dynamics of Vector-Host Feeding Contact Rate with Saturation: A Case of Malaria in Western Kenya. Scientific Research Publishing. 4(10):1381-1391. AbstractWebsite

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.

2012

Wairimu, J.  2012.  Mathematical analysis and dynamical systems : modeling Highland malaria in western Kenya. Abstract

The objective of this thesis is to model highland malaria in western Kenya using dynamical systems. Two mathematical models are formulated ; one, on differentiated susceptibility and differentiated infectivity in a metapopulation setting with age structure, the other, a saturated vector feeding rate model with disease induced deaths and varying host and vector populations. In the first model, we consider the different ecosystems identified as malaria hotspots in the western Kenya highlands and consider the ecosystems as different patches. The population in each patch is classified as, either child or, adult. The model will aid in examining the role of ecosystem heterogeneity and age structure to the persistent malaria epidemics in the highlands. We formulate the differentiated susceptibility and infectivity model that extend to multiple patches the well known epidemiological models in one patch. Classifying the hot spots as n patches, we give its mathematical analysis using the theory of triangular system, monotone non-linear dynamical systems, and Lyapunov-Lasalle invariance principle techniques. Key to our analysis is the definition of a reproductive number, Ro, the number of new infections caused by one individual in an otherwise fully susceptible population throughout the duration of the infectious period. The existence and stability of disease-free and endemic equilibrium is established. We prove that the disease free state of the systems is globally asymptotically stable when the basic reproduction number Ro<1, and when Ro>1 an endemic equilibrium is established which is locally and globally asymptotically stable. The model shows that the age structuring reduces the magnitude of infection. Using relevant data we did some simulation, to demonstrate the role played by metapopulation and age structuring on the incidence and Ro. In the second part we formulate a model for malaria with saturation on the vector feeding rates that lead to a nonlinear function in the infection term. The vector feeding rate is assumed, as in the predator prey models, to rise linearly as a function of the host-vector ratio until it reaches a threshold Qv, after which the vector feeds freely at its desired rate. The two populations are variable and drive malaria transmission, such that when the vectors are fewer than hosts, the rate of feeding is determined by the vectors feeding desire, whereas, when the hosts are more than the vectors, the feeding rate is limited by host availability and other feeding sources may have to be sought by the vector. Malaria induced deaths are introduced in the host population, while the vector is assumed to survive with the parasite till its death. We prove that the Disease Free Equilibrium is locally and globally asymptotically stable if Ro<1 and when Ro>1, an endemic equilibrium emerges, which is unique, locally and globally asymptotically stable. The role of the saturated mosquito feeding rate is explored with simulation showing the crucial role it plays especially on the basic reproduction number

Wairimu, JK, Sallet GWO.  2012.  A vector SIS model for malaria in a patchy environment with age structure. School of Biological Sciences. 2012Website

2010

Fredrick Ongowe, Sophie Hennequin, Josephine Kagunda Wairimu, Nyoungue Aimé, Mamadou Lamine Diouf, Mouhamadou Diaby, Abderrahman Iggidr, Mamadou Sy, Salle G.  2010.  Biomathematics modelling for the study of failures propagation: Application to a production resource.

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