Browsing by Author "Virginia Kitetu"

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    Mathematical Modelling of COVID-19 Transmission in Kenya: A Model with Reinfection Transmission Mechanism
    (HINDAWI, 2021-10-16) Isaac Mwangi Wangari; Stanley Sewe; George Kimathi; Mary Wainaina; Virginia Kitetu; Winnie Kaluki
    In this study we propose a Coronavirus Disease 2019 (COVID-19) mathematical model that stratifies infectious subpopulations into: infectious asymptomatic individuals, symptomatic infectious individuals who manifest mild symptoms and symptomatic individuals with severe symptoms. In light of the recent revelation that reinfection by COVID-19 is possible, the proposed model attempt to investigate how reinfection with COVID-19 will alter the future dynamics of the recent unfolding pandemic. Fitting the mathematical model on the Kenya COVID-19 dataset, model parameter values were obtained and used to conduct numerical simulations. Numerical results suggest that reinfection of recovered individuals who have lost their protective immunity will create a large pool of asymptomatic infectious individuals which will ultimately increase symptomatic individuals with mild symptoms and symptomatic individuals with severe symptoms (critically ill) needing urgent medical attention. The model suggests that reinfection with COVID-19 will lead to an increase in cumulative reported deaths. Comparison of the impact of non pharmaceutical interventions on curbing COVID19 proliferation suggests that wearing face masks profoundly reduce COVID-19 prevalence than maintaining social/physical distance. Further, numerical findings reveal that increasing detection rate of asymptomatic cases via contact tracing, testing and isolating them can drastically reduce COVID-19 surge, in particular individuals who are critically ill and require admission into intensive care.
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    Mathematical Modelling of the Dynamics of the Spread of Schistosomiasis Incorporating Protection of Humans
    (International Journal of Recent Research in Mathematics Computer Science and Information Technology, 2021-09) Sr Mary Nyambura Mwangi; Isaac Mwangi; Virginia Kitetu
    Schistosomiasis, also known as Bilharziasis, is a parasitic disease of global concern, and is among the neglected tropical diseases. It is caused by the digenetic trematode flukes of the genus Schistosoma and transmitted by fresh water snails of the family Planorbidae. Its clinical manifestation depends on the immunity of the person, the warm burden and the duration of the same worms in the body. African countries suffer greatly from this disease. We have formulated a mathematical model with four compartments, Susceptible-Protected-Infected-Treated, (SPIT), and the corresponding ordinary differential equations in an attempt to investigate the impact of human protection. The disease free equilibrium and endemic equilibrium have been analyzed. The stability of the disease free equilibrium has also been determined. The reproduction number has been determined using the next Generation matrix. Mathematical simulation was carried out. The impact of human protection on the dynamics of the spread of the disease has been analyzed. Our results show that protection of the human being plays a great role in controlling the spread of this disease. It contributes significantly to reduction of infections and the stability of the susceptible population.
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    Modeling in Mathematics in Estimation and Prediction of the Coronavirus Infections in Kitui County. A Case with Isolation of the Vulnerable
    (International Journal of Novel Research in Physics Chemistry & Mathematics, 2022-08-16) Grace Mumbanu Maithya; Winnie Kaluki; Virginia Kitetu
    People’s lives have been affected socially by the coronavirus around the globe. Because of its social and economic impact, some measures for the prevention of the disease have been placed so that the spread can reduce. Quarantine, social distancing, and social distancing are some of the control measures. One that is considered to be very effective is for the vulnerable population to be isolated. A Model including six compartments was developed so that the number of people recovering may increase, so to achieve this vulnerable population was isolated. These six compartments are namely below; Susceptible, Exposed, Infected, Quarantined, Isolation of Vulnerable, and Recovered. Formulation of endemic equilibrium points, disease-free equilibrium, and local stability of disease-free equilibrium were theoretically proved. By use of the next generation matrix, derivation of basic reproductive number which is abbreviated as Rₒ was done. There is THE stability of disease-free equilibrium which is also abbreviated as a disease-free equilibrium when the basic reproductive number is less than one, which is 𝑹𝟎<𝟏. There is the stability of endemic equilibrium, the endemic equilibrium point when the basic reproductive number is greater than one, which is 𝑹𝟎>𝟏. There is instability in disease-free equilibrium when 𝑹𝟎>𝟏. Susceptible, Exposed, Infected, Isolated Vulnerable and Recovered population model was solved numerically by Runge Kutta 4th order; the drawn graphs also showed that when the vulnerable population is isolated there is an increment in the number of people who recover and a reduction in deaths. More isolation Centers so as to isolate vulnerable populations to recover more is recommended whereby the world health organization and ministry of health in Kenya need to put it in place.