Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach
Abstract
1. Introduction
2. Model Formulation
3. Model Analysis
3.1. Key Definition of Caputo-Fractional Derivatives
3.2. Existence and Uniqueness of Solution
3.3. Numerical Scheme for Model (4) in Caputo Sense
4. Basic Properties
4.1. Positivity of Solutions
4.2. Boundedness of Trajectories
- We have the following result about the boundedness of trajectories of system .
4.3. Basic Reproduction Number and Existence of Equilibria
5. Results and Discussion
5.1. Model Validation
5.2. Sensitivity Analysis
5.3. Effect of Memory on the Disease Transmission
5.4. Impact of Insecticides Use on HAT Transmission
5.5. Impact of Prevention Measures on the Disease Dynamics
5.6. Impact of Human Awareness on HAT Transmission
6. Concluding Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model Parameter | Definition |
---|---|
Rate of infection from humans to tsetse flies | |
Rate of infection from cattle to tsetse flies | |
Infection rate from tsetse flies to humans | |
Infection rate from tsetse flies to cattle | |
Rate at which recovered humans become susceptible again | |
Rate at which recovered cattle become susceptible again | |
Death rate in humans due to the disease | |
Death rate in cattle due to the disease | |
Natural death rate in humans | |
Natural death rate in cattle | |
Natural death rate in tsetse flies | |
Frequency of bites by tsetse flies on hosts | |
Recovery rate in humans | |
Recovery rate in cattle | |
Rate at which exposed humans become infectious | |
Rate at which exposed cattle become infectious | |
Rate at which exposed tsetse flies become infectious | |
Awareness acquisition rate in humans | |
Implementation rate of protective actions | |
Insecticide application rate |
Symbol | Definition | Value | Units | Source |
---|---|---|---|---|
Rate of infection from humans to tsetse flies | [34,45] | |||
Rate of infection from cattle to tsetse flies | [34,45] | |||
Infection rate from tsetse flies to humans | [34,45] | |||
Infection rate from tsetse flies to cattle | [34,45] | |||
Rate at which recovered humans become susceptible again | [34,46] | |||
Rate at which recovered cattle become susceptible again | [34,46] | |||
Death rate in humans due to the disease | [3,45] | |||
Death rate in cattle due to the disease | [3,45] | |||
Natural death rate in humans | [3,46] | |||
Natural death rate in cattle | [3,46] | |||
Natural death rate in tsetse flies | [3,46] | |||
Frequency of bites by tsetse flies on hosts | [3,46] | |||
Recovery rate in humans | [3,46] | |||
Recovery rate in cattle | [3,46] | |||
Rate at which exposed humans become infectious | [3,46] | |||
Rate at which exposed cattle become infectious | [3,46] | |||
Rate at which exposed tsetse flies become infectious | [3,46] | |||
Awareness acquisition rate in humans | variable | fitted | ||
Implementation rate of protective actions | variable | fitted | ||
Insecticide application rate | variable | fitted |
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Koga, O.; Mayengo, M.; Helikumi, M.; Mhlanga, A. Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach. AppliedMath 2025, 5, 127. https://doi.org/10.3390/appliedmath5030127
Koga O, Mayengo M, Helikumi M, Mhlanga A. Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach. AppliedMath. 2025; 5(3):127. https://doi.org/10.3390/appliedmath5030127
Chicago/Turabian StyleKoga, Oscar, Maranya Mayengo, Mlyashimbi Helikumi, and Adquate Mhlanga. 2025. "Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach" AppliedMath 5, no. 3: 127. https://doi.org/10.3390/appliedmath5030127
APA StyleKoga, O., Mayengo, M., Helikumi, M., & Mhlanga, A. (2025). Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach. AppliedMath, 5(3), 127. https://doi.org/10.3390/appliedmath5030127