Browsing by Author "Helikumi, Mlyashimbi"

Now showing 1 - 6 of 6
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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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    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 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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    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