Browsing by Author "Mhlanga, Adquate"

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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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    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