Browsing by Author "Lolika, Paride O."

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    An Intrinsic Analysis of Human Brucellosis Dynamics in Africa
    (ResearchGate, 2022-08-27) Lolika, Paride O.; Helikumi, Mlyashimbi
    Brucellosis is one of the most common zoonotic infections globally. It affects humans, domestic animals and wildlife. In this paper, we conduct an intrinsic analysis of human brucellosis dynamics in non-periodic and periodic environments. As such we propose and study two mathematical models for human brucellosis transmission and control, in which humans acquire infection from cattle and wildlife. The first model is an autonomous dynamical system and the second is a non-autonomous dynamical system in which the seasonal transmission of brucellosis is incorporated. Disease intervention strategies incorporated in this study are cattle vaccination, culling of infectious cattle and human treatment. For both models we conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. Using sensitivity analysis we established that R0 is most sensitive to the rate of brucellosis transmission from buffalos to cattle, the result suggest that in order to control human brucellosis there is a need to control cattle infection. Based on our models, we also formulate an optimal control problem with cattle vaccination and culling of infectious cattle as control functions. Using reasonable parameter values, numerical simulations of the optimal control demonstrate the possibility of reducing brucellosis incidence in humans, wildlife and cattle, within a finite time horizon, for both periodic and non-periodic environments.
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    Dynamics and Analysis of Chronic Brucellosis in Sheep
    (Journal of Advances in Mathematics and Computer Science, 2020-08-30) Lolika, Paride O.; Helikumi, Mlyashimbi
    We proposed and studied a new fractional-order model for the transmission dynamics of brucellosis with a special focus on the sheep-to-sheep transmission. Two control strategies namely; culling and vaccination rate are incorporated in the model. We computed the basic reproduction number R0 and we studied the global stability of disease-free and endemic equilibrium point in terms of basic reproduction number R0. We found that both the disease-free and endemic equilibrium points are globally stable whenever R0 < 1 and R0 > 1 respectively. In numerical simulations, we performed the sensitivity analysis of the model and expressed the relationship between model parameters and R0. We noted that, increase on the magnitude of model parameters with negative correlation coefficients would significantly reduce the spread of Brucellosis disease in the population. Moreover, model validation and parameter estimation for fractional-order and classical integer-order derivatives was carried out using real brucellosis for Egypt, 1999-2011. Overall, we noted that fractional-order model gave better prediction of brucellosis compared to classical integer-order model. Furthermore, we investigated the role of memory effects on the transmission of brucellosis in the population. We observe that, the memory effects have influence on the transmission of brucellosis in the community. In addition, we noted that the aforementioned control strategies have the potential to reduce the transmission of brucellosis in the population. In particular, we observed that whenever the culling and vaccination rate is greater than 40% and 50% respectively, the disease dies out in the population.
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    Dynamics and Analysis of COVID-19 Disease Transmission: The Effect of Vaccination and Quarantine
    (AIMS, 2023-09-01) Helikumi, Mlyashimbi.; Lolika, Paride O.
    In this study, a fractional-order model for COVID-19 disease transmission is proposed and studied. First, the disease-free equilibrium and the basic reproduction number, R0 of the model has been communicated. The local and global stability of the disease-free equilibrium have been proved using well-constructed Lyapunov functions. Moreover, a normalized sensitivity analysis for the model parameters has been performed to identify their influence on R0. Real data on COVID-19 disease from Wuhan in China has been used to validate the proposed model. Finally, a simulation of the model has been performed to determine the effects of memory and control strategies. Overall, one can note that vaccination and quarantine have the potential to minimize the spread of COVID-19 in the population.
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    Global Dynamics of Fractional-order Model for Malaria Disease Transmission
    (Asian Research Journal of Mathematics, 2022) Helikumi, Mlyashimbi; Lolika, Paride O.
    In this study, we formulated and analyzed a fractional-order model for malaria disease transmission using Atangana-Beleanu-Caputo in sense to study the effects of heterogeneity vector biting exposure on the human population. To capture effects the heterogeneity vector biting exposure, we sub-divided the human population into two sub-groups namely; the population in high and low risk areas. In the model analysis, we computed the basic reproduction number R0 and qualitatively used to assess the existence and extinction of disease in the population. Additionally, we used the fixed point theorem to prove the existence and uniqueness of solutions. Numerical schemes for both Euler and Adam-Bathforth-Moulton are present in details and used in model simulations. Furthermore, we performed the numerical simulation to support the analytical results in this study. From numerical simulations, we estimated the values of model parameters using least square fitting method for the real data of malaria reported in Zimbabwe. The sensitivity analysis of the model parameters was done to determine the correlation between model parameters and R0. Finally, we used the Euler and Adam-Bashforth-Moulton scheme to simulate the model system using estimated parameters. Overall, we noted that fractional-order derivatives have more influence on the dynamics of malaria disease in the population.
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    Global Dynamics of Fractional-order Model for Malaria Disease Transmission
    (Asian Research Journal of Mathematics, 2022-07-09) Helikumi, Mlyashimbi; Lolika, Paride O.
    In this study, we formulated and analyzed a fractional-order model for malaria disease transmission using Atangana-Beleanu-Caputo in sense to study the effects of heterogeneity vector biting exposure on the human population. To capture effects the heterogeneity vector biting exposure, we sub-divided the human population into two sub-groups namely; the population in high and low risk areas. In the model analysis, we computed the basic reproduction number R0 and qualitatively used to assess the existence and extinction of disease in the population. Additionally, we used the fixed point theorem to prove the existence and uniqueness of solutions.Numerical schemes for both Euler and Adam-Bathforth-Moulton are present in details and used in model simulations. Furthermore, we performed the numerical simulation to support the analytical results in this study. From numerical simulations, we estimated the values of model parameters using least square fitting method for the real data of malaria reported in Zimbabwe. The sensitivity analysis of the model parameters was done to determine the correlation between model parameters and R0. Finally, we used the Euler and Adam-Bashforth-Moulton scheme to simulate the model system using estimated parameters. Overall, we noted that fractional-order derivatives have more influence on the dynamics of malaria disease in the population