Papers by Frankline Tireito
Science Mundi, Nov 29, 2023
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Applied Mathematical Sciences, 2018
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Discrete Dynamics in Nature and Society
In this paper, a within-host cholera mathematical model has been developed using a system of ordi... more In this paper, a within-host cholera mathematical model has been developed using a system of ordinary differential equations incorporating vaccine efficacy. The formulated model considers cells in an already vaccinated individual with a vaccine whose efficacy is γ . The solutions of the model have been shown to be both positive and bounded hence well-posed. The vaccine basic reproduction number has been carried out using the next generation matrix approach and is given by R 0 V = γ / d + μ 2 and R 0 V < 1 if γ < d + μ 2 . Analysis of the model shows that i n f e c t i o n f r e e e q u i l i b r i u m I F E point is both locally and globally asymptotically stable when R 0 V < 1 and i n f e c t i o n e q u i l i b r i u m I E point is locally asymptotically stable when R 0 V > 1 . Furthermore, analysis of the model shows that R 0 V < 1 is not sufficient enough to eradicate in-host cholera disease, hence the existence of backward bifurcation which is an indication...
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Asian Research Journal of Mathematics
Discrete age structured models provide a better approach of discussing the spread of infectious d... more Discrete age structured models provide a better approach of discussing the spread of infectious diseases with infectivity, mortality and recovery being age dependent. Measures such as vaccination are carried out in discrete time or applied to individuals in certain age-groups. In the past Ebola Virus disease (EVD) outbreaks, infections in children under 5 years was associated with high mortality rates. In this work, a general discrete SVEIR epidemic model with age structure is formulated. The study establishes the existence of the endemic equilibrium and further shows that it is globally stable using the graph theoretic approach on the method of Lyapunov functions. The model is then applied to EVD dynamics to study the impact of vaccination on the age structured population. The numerical simulation of the discrete age case scenario demonstrates that vaccination of children under 5 years of age against EVD has a great impact in reducing their susceptibility because of the active immu...
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Journal of Advances in Mathematics and Computer Science
Alcohol addiction is a phenomenon that has attracted the attention of numerous researchers and ac... more Alcohol addiction is a phenomenon that has attracted the attention of numerous researchers and academics in a variety of professions due to its serious repercussion on all spheres of human life. Alcoholism is a common addiction in adults throughout the globe. Hence there is need to target efficient preventative and therapeutic measures.The impact of media awareness and treatment on the drinking behavior of various drinker classes is discussed in several mathematical models. Nevertheless, the impact of the exposed class of alcoholics on light and heavy drinkers in the presence of media awareness, has not been addressed. The model was formulated based on a system of differential equations. To perform stability analysis of the model at each equilibrium point, Jacobian matrix method was employed. By use of MATLAB, numerical simulations on the impact of awareness on alcoholism were performed. Secondary data obtained from NACADA and data from rehabilitation centers in Kenya was used to va...
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Journal of Advances in Mathematics and Computer Science
In this paper, a mathematical model for COVID-19 disease incorporating clinical management based ... more In this paper, a mathematical model for COVID-19 disease incorporating clinical management based on a system of Ordinary Differential Equations is developed. The existence of the steady states of the model are determined and the effective reproduction number derived using the next generation matrix approach. Stability analysis of the model is carried out to determine the conditions that favour the spread of COVID-19 disease in a given population. The Disease Free Equilibrium is show to be locally asymptotically stable when \(R\)e < 1 and the Endemic Equilibrium is locally asymptotically stable when \(R\)e > 1. The Disease Free Equilibrium is shown not to be globally asymptotically stable using a technique by Castillo Chavez and the Endemic Equilibrium is shown to be globally asymptotically stable by means of Lyapunov's direct method and LaSalle's invariance principle. This implies that COVID-19 disease transmission can be kept low or manageable with the incorporation o...
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International Mathematical Forum, 2016
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Approximately 198 million cases of malaria manifested worldwide in 2013, causing 584,000 deaths, ... more Approximately 198 million cases of malaria manifested worldwide in 2013, causing 584,000 deaths, further solidifying malaria’s status as a serious global health predicament. A vast array of immunopotentiating molecules like unmethylated CpG motif oligodeoxynucleotides (ODNs) operate in concert with cytokines in rendering hosts resistant to parasitic infections. The CpG ODNs exert potent immunostimulatory effects via nexus with dendritic cell Toll-like receptors (TLRs) like TLR 9 and by activating immune cells like B-cells and NK cells. Investigations were performed to resolve the anti-malarial effects of cytokine-CpG ODN co-inoculation in BALB/c mice infected with Plasmodium berghei ANKA strain. Two BALB/c mice groups were infected with virulent P. berghei ANKA strain parasites, followed by five consecutive days of cytokine-CpG ODN co-therapies. Six control groups with various regimen were included. Parasitaemia, and clinico-haematological outcomes accompanying the immunotherapies w...
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In this paper we fit a time series model that best describes the rainfall pattern of Uasin Gishu ... more In this paper we fit a time series model that best describes the rainfall pattern of Uasin Gishu county from the general ARIMA family and generate the values (p,d,q)(P,D,Q)s. The model that best fitted the Kapsoya historical rainfall data was SARIMA (0,0,0)(,0,1,2)12. This model is used to forecast average expected monthly rainfall statistics for two years. For verification and data fitting to the model, R computer software was employed. The data used is real rainfall data from Kapsoya meteorological station in Uasin Gishu County.
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International Mathematical Forum, 2016
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IOSR Journal of Mathematics, 2016
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Papers by Frankline Tireito