Browsing by Author "Helikumi, Mlyashimbi"

Now showing 1 - 12 of 12
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    Afractional-Order Trypanosomabrucei Rhodesiense Model With Vector Saturation and Temperature Dependent Parameters
    (SPRINGER, 2020) Helikumi, Mlyashimbi; Kgosimore, Moatlhodi; Kuznetsov, Dmitry; Mushayabasa, Steady
    and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even Temperature is one of the integral environmental drivers that strongly affect the distribution zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximumtemperature. In this study, a fractional-order Trypanosomabrucei rhodesiense model incorporating vector saturation and temperature dependent parameters is considered. The proposed model incorporates the interplay between vectors and two hosts, humans and animals. We computed the basic reproduction number andestablished results on the threshold dynamics. Meanwhile, we explored the effects of vector control and screening of infected host on long-term disease dynamics. We determine threshold levels essential to reducing the basic reproduction number to level below unity at various temperature levels. Our findings indicate that vector control and host screening could significantly control spread of the disease at different temperature levels.
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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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    Dynamical Analysis of Mpox Disease with Environmental Effects
    (MDPI, 2025-05-29) Helikumi, Mlyashimbi; Ojija, Fredrick; Mhlanga, Adquate
    In this study, we develop a fractional-order mathematical model for investigating the transmission dynamics of monkeypox (Mpox), accounting for interactions between humans, rodents, and environmental reservoirs. The model uniquely integrates two key control strategies—public health awareness and environmental sanitation—often over- looked in previous models. We analyze the model’s well-posedness by establishing the existence, uniqueness, and positivity of solutions using the fixed-point theorem. Using data from the Democratic Republic of Congo, we estimate the model parameters and demon- strate that the fractional-order model (φ = 0.5) fits real-world data more accurately than its integer-order counterpart (φ = 1). The sensitivity analysis using partial rank correlation coefficients highlights the key drivers of disease spread. Numerical simulations reveal that the memory effects inherent in fractional derivatives significantly influence the epidemic’s trajectory. Importantly, our results show that increasing awareness (ε) and sanitation efforts (η) can substantially reduce transmission, with sustained suppression of Mpox when both parameters exceed 90%. These findings highlight the synergistic impact of behavioral and environmental interventions in controlling emerging zoonotic diseases.
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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 of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class
    (Hindawi, 2022) Helikumi, Mlyashimbi; Eustace, Gideon; Mushayabasa, Steady
    In this paper, a nonlinear fractional-order chikungunya disease model that incorporates asymptomatic infectious individuals is proposed and analyzed. The main interest of this work is to investigate the role of memory effects on the dynamics of chikungunya. Qualitative analysis of the model’s equilibria showed that there exists a threshold quantity which governs persistence and extinction of the disease. Model parameters were estimated based on the 2015 weekly reported cases in Colombia. The Adams-Bashforth-Moulton method was used to numerically solve the proposed model. We investigated the role of asymptomatic infectious patients on short- and long-term dynamics of the diseases. We also determined threshold levels for the efficacy of preventative strategies that results in effective management of the disease. We believe that our model can provide invaluable insights for public health authorities to predict the effect of chikungunya transmission and analyze its underlying factors and to guide new control efforts.
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    Effect of Global Climate Change on Insect Populations, Distribution, and its Dynamics
    (ELSEVIER, 2025-07-07) Ojija, Fredrick; Mng’ong’o, Marco; Aloo, Becky N.; Mayengo, Gabriel; Helikumi, Mlyashimbi
    Insects are vital to various ecosystems as pollinators, decomposers, and food sources for many organisms. They dominate diverse terrestrial (e.g., glassland) and aquatic (lakes, oceans, rivers, etc.) ecosystems. Previous studies report that more than half of the estimated 2.0 million species of living organisms identified on our planet are insects. However, global climate change (GCC), characterised by rising temperatures and altered precipitation patterns, significantly impacts their populations worldwide. We reviewed the literature to provide an overview of GCC events in insects. Collectively, the study findings reveal that global temperature and precipitation change are among the extreme GCC events affecting more than 30% of insect population, distribution, physiology, feeding habits, interactions, migration, and communication across the globe. The climate change intensifies insect cycles and insect damage in agroecosystems. In response, insect species alter their geographic ranges and phenology, changing population dynamics and interactions. GCC also influences reproductive patterns, including mating behaviour and breeding synchrony. Warmer global temperatures might advance or delay insect emer- gence, causing mismatches with food availability or pollination partners. While some insect populations may adapt, extreme heat events or prolonged droughts exceeding their physiological tolerance result in population declines or local extinctions. Predictions suggest that up to 65% of insect populations could face extinction within the next century due to increasing climate change. Thus, understanding these impacts is essential for predicting the ecological consequences of the GCC and developing effective conservation strategies to mitigate such impacts and protect insect biodiversity and ecosystem services
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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
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    Global Stability Analysis of a Fractional-Order Ebola Epidemic Model with Control Strategies
    (2024-02-13) Lolika, Paride O; Helikumi, Mlyashimbi; Jomah, Sulieman A. S; Bakhet, Mohamed Y. A.; Galla, Kennedy Crispo; Kheiralla, Awad Hussien
    We proposed a fractional-order derivative model for Ebola virus disease (EVD) to assess the effects of control strategies on the spread of the disease in the population. The proposed model incorporates all relevant biological factors, health education campaigns, prevention measures, and treatment as control strategies. We computed the basic reproduction number R0 and qualitatively used it to assess the existence of the model states. In particular, we noted that two equilibrium points exist, the disease-free and endemic equilibrium points which are both globally stable whenever R0 < 1 and R0 > 1 respectively. We performed sensitivity analysis on the key parameters that drive the EVD dynamics to determine their relative importance in EVD transmission and prevalence. Model parameters were estimated using the 2014 Ebola outbreak in Guinea. Further, numerical simulation results are presented using fractional Adam-Bashforth-Moulton scheme to support the analytical findings. From the numerical simulations, we have noted that as α decreases from unit, the solution profiles of the model attain its stability much faster than at α = 1. Furthermore, the results demonstrated that the aforementioned control strategies have the potential to reduce the transmission of EVD in the population.
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    Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach
    (MDPI, 2025-09-22) Koga, Oscar; Mayengo, Maranya; Helikumi, Mlyashimbi; Mhlanga, Adquate
    In this research work, we proposed and studied a fractional-order model for Human African Trypanosomiasis (HAT) disease transmission, incorporating three control strategies: health education campaigns, prevention measures, and use of insecticides. The theoretical analysis of the model was presented, including the computation of disease-free equilibrium and basic reproduction number. We performed the stability analysis of the model and the results showed that the disease-free equilibrium point was locally asymptotically stable whenever R0 < 1 and unstable when R0 > 1. Furthermore, we performed parameter estimation of the model using HAT-reported cases in Tanzania. The results showed that fractional-order model had a better fit to the real data compared to the classical integer order model. Sensitivity analysis of the basic reproduction number was performed using computed partial rank correlation coefficients to assess the effects of parameters on HAT transmission. Additionally, we performed numerical simulations of the model to assess the impact of memory effects on the spread of HAT. Overall, we observed that the order of derivatives significantly influences the dynamics of HAT transmission in the population. Moreover, we simulated the model to assess the effectiveness of proposed control strategies. We observed that the use of insecticides and prevention measures have the potential to significantly reduce the spread of HAT within the population.
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    Modeling the Effects of Treatment Adherence Challenges on the Transmission Dynamics of Hepatitis C Virus
    (OPEN ACCESS, 2025-08-08) Mupedza, Tinashe Victor; Mhlanga, Laurette; Mamutse ,Dennis; Helikumi, Mlyashimbi; Oresto ,Lolika Paride; Tangakugara, Murambiwa Shingirai; Mhlanga, Adquate
    Infectious Disease Modeling is Crucial for Predicting Disease Progression Over Time And Helps Guide Decision Makers in Public Health Policy. Hepatitis C Virus (HCV) Prevalence is Still IncreasingiIn Zimbabwe, A Low-Middle-Income Country (LMIC), Despite The Avail- Ability of Effective Treatments, and the Reasons for this Increase Are Not Well Understood. Our Study Employed a Mathematical Model to Explain the Impact of Poor Treatment Adher- Ence on HCV Transmission Dynamics in Zimbabwe. we Computed The Basic Reproduc- Tion Number (R0), a Vital Metric of Disease Spread. Equilibrium States of the Model Were Determined, And Their Stability Was Investigated. The Study Demonstrated That An Adher- Ence Level Exceeding 52% Causes the Reproduction Number to Drop Below 1, Curtailing Further Spread. Our HCV Model Indicates that Variations in Re-Susceptibility Minimally Impact Outcomes, Suggesting that Re-Susceptibility Can Often be Excluded in Such Analy- Ses. Our Model Unraveled the Synergistic Impact of Simultaneously Enhancing the Recov- Ery Rate of Acutely Infected Individuals and Treatment Adherence on Reducing R0. the Study Underlines the Pressing Need for Stronger Health Interventions, Including Patient Education, Financial Assistance, and Rigorous Monitoring, To Improve Treatment Adher- Ence. These Interventions are Paramount in Curbing HCV Proliferation, Particularly in Lmics Like Zimbabwe, and Can Serve as aTemplate for Similar Settings Globally
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    Optimal Control Applied to a Stage-structured Cassava Mosaic Disease Model with Vector Feeding Behavior
    (ELSEVIER, 2025) Lusekelo, Eva; Helikumi, Mlyashimbi; Daudi, Salamida; Mushayabasa, Steady
    Cassava remains Sub-Saharan Africa’s secondmost crucial staple food crop after maize. However production of sufficient yields is hampered by pests and diseases. In particular, the white fly (Bemisia tabaci)has the potential toreduceexpectedyieldsby50%since it directly damages cassava leaves by feeding on phloem, causing chlorosis and abscission. This study develops an ovel mathematical model for cassava mosaic disease that incorporates immature and adult white fly populations. Additionally, the model includes vector feeding behavior since priorstudieshaveshownthatvectorsexhibitpreferencestosettleforeitherhealthyorinfected hosts.Wedeterminedtheoffspringnumberandcarriedoutitssensitivityanalysis.Additionally, we carried out an optimal control study on the use of insecticides and plantroguing as disease control measures against cassava mosaic disease .Our results show that vector preference and efficiency of disease control strategies plays an important role in shaping the short and long term dynamics of cassava mosaic disease, which subsequently impacts the design of its optimal control strategies