Browsing by Author "Helikumi, Mlyashimbi"

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Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model
(MDPI, 2019-10-14) Helikumi, Mlyashimbi; Kgosimore, Moatlhodi; Kuznetsov, Dmitry; Mushayabasa, Steady
In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns
Dynamic modelling and optimal control analysis of a fractional order chikungunya disease model with temperature effects
(Elsevier, 2023-01-19) Lusekelo, Eva; Helikumi, Mlyashimbi; Kuznetsov, Dmitry; Mushayabasa, Steady
Approximately 1.3 billion inhabitants in 94 countries are estimated to be at risk of chikungunya virus infection. A mechanistic compartmental model based on fractional calculus, the Caputo derivative has been proposed to evaluate the effects of temperature and multiple disease control measures (larvicides use, insecticides and physical barriers) during an outbreak. The proposed model was calibrated based on data from literature and validated with daily chikungunya fever cases reported at Kadmat primary health centre, India. The transmission potential of the disease was examined. Sensitive analyses were conducted through computing partial rank correlation coefficients. Memory effects which are often neglected when mechanistic models are used to model the transmission dynamics of infectious diseases, were found to have a significant effect on the dynamics of chikungunya.
Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model
(AIMS Press, 2020-02-27) Helikumi, Mlyashimbi; Kgosimore, Moatlhodi; Kuznetsov, Dmitry; Mushayabasa, Steady
The e ects of seasonal variations on the epidemiology of Trypanosoma brucei rhodesiense disease is well documented. In particular, seasonal variations alter vector development rates and behaviour, thereby influencing the transmission dynamics of the disease. In this paper, a mathematical model for Trypanosoma brucei rhodesiense disease that incorporates seasonal e ects is presented. Owing to the importance of understanding the e ective ways of managing the spread of the disease, the impact of time dependent intervention strategies has been investigated. Two controls representing human awareness campaigns and insecticides use have been incorporated into the model. The main goal of introducing these controls is to minimize the number of infected host population at low implementation costs. Although insecticides usage is associated with adverse e ects to the environment, in this study we have observed that by totally neglecting insecticide use, e ective disease management may present a formidable challenge. However, if human awareness is combined with low insecticide usage then the disease can be e ectively managed.
A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters
(Springer Nature, 2020-06-11) Helikumi, Mlyashimbi; Kgosimore, Moatlhodi; Kuznetsov, Dmitry; Mushayabasa, Steady
Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximum temperature. In this study, a fractional-order Trypanosoma brucei 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 and established 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.
Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: AFractional-Order Model Approach
(MDPI, 2025-09-25) 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.
Modeling the effects of temperature and heterogeneous biting exposure on chikungunya virus disease dynamics
(Elsevier, 2022-07-06) Lusekelo, Eva; Helikumi, Mlyashimbi; Kuznetsov, Dmitry; Mushayabasa, Steady
Within the last decades, chikungunya virus (CHIKV), a mosquito-borne arboviral disease transmitted by Aedes species mosquitoes has been a growing public health burden. Approximately 1.3 billion inhabitants in 94 countries are estimated to be at risk of chikungunya virus infection. Prior studies suggest that temperature and heterogeneous biting exposure are some of the key determinant factors in transmission dynamics of vector-borne diseases. In order to direct preparedness for future outbreaks, it is imperative to evaluate the effects of heterogeneous biting exposure and temperature variations on transmission dynamics of CHIKV. In this paper, a mathematical model that incorporates heterogeneous biting exposure and temperature effects has been developed and analyzed. The basic reproduction number, an important metric for infectious disease models has been determined. Data from literature has been used to calibrate the model and observed CHIKV data for Kadmat primary health centre, India (2 July to 7 September 2007) has been used to validate the model. Results from the study suggest that disease prevention strategies which are effective at stopping transmission of CHIKV more than 80% of the time, will be highly effective minimizing disease burden during outbreaks. The proposed model can be used to inform policy makers on effective ways of managing CHIKV during outbreaks.
Quantifying the effects of temperature and predation on the growth of Aedes mosquito population
(Springer Nature, 2023-01-10) Lusekelo, Eva; Helikumi, Mlyashimbi; Kuznetsov, Dmitry; Mushayabasa, Steady
Despite having been tested in multiple settings, the quantitative impact of predatory aquatic insects to reduce mosquito population remains unclear. To address this question, an ecological model of Aedes mosquito population incorporating temperature-dependent entomological parameters and predation is developed. The vector reproduction number is derived and entomological parameters that strongly influence it have been identified. Implications of predation on mosquito growth are examined. Results show that predators with high daily attack rate can significantly reduce vector reproduction to extremely low values close to zero. The study provides a framework for more detailed, predator specific studies that are essential to develop an improved understanding on the relationship between predatory aquatic insects and Aedes mosquitoes.