Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach

Copyright © Author(s) 2025. All Rights Reserved. Published by GLOBAL PUBLICATION HOUSE | International Journal Applied Science Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-BashforthMoulton Approach By Author(s): Musa Yunusa¹˒², Omale David¹, Joseph Egbemhenghe³, Godwin Onuche Acheneje¹˒², William Atokolo¹˒²* ¹ Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria ² Laboratory of Mathematical Epidemiology, Prince Abubakar Audu University, Anyigba ³ Department of Mathematics Education, Prince Abubakar Audu University, Anyigba, Nigeria Corresponding author: [email protected] Abstract: Trypanosomiasis remains a critical vector-borne disease burden, especially in sub-Saharan African communities where tsetse fly populations thrive and healthcare infrastructure remains limited. Conventional integer-order mathematical frameworks frequently inadequately represent the hereditary characteristics and intricate transmission patterns inherent in vector-borne disease systems. This research presents a fractional-order mathematical framework for examining the epidemiological characteristics of trypanosomiasis transmission, with particular focus on how treatment interventions at different disease stages affect overall transmission dynamics. The primary goal is to explore how variations in treatment efficacy rates and vector-human contact patterns influence disease persistence and spread within affected populations. The framework employs fractional derivatives to more accurately capture the non-Markovian properties of infection progression and immune response mechanisms. The computational results further reveal that strategically implemented treatment protocols can dramatically reduce infection prevalence, potentially driving the system toward disease elimination scenarios. The innovation of this work centers on applying fractional calculus to trypanosomiasis transmission modeling, an approach relatively unexplored in this epidemiological context, while simultaneously incorporating multi-stage treatment interventions and natural immunity waning processes. The model demonstrates superior precision in representing temporal disease progression compared to classical integer-order approaches. This investigation underscores the utility of fractional-order modeling in vector-borne disease research and emphasizes the critical importance of strengthening treatment capacity and vector control measures to effectively manage and eliminate trypanosomiasis transmission in endemic regions. Keywords: Trypanosomiasis, Fractional-order analysis, Adam-Bashforth-Moulton, Numerical Simulations. How to cite: Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 Page 12 of 26 ARTICLE ID: #02163 10.5281/ZENODO.17621884 e-ISSN 3050-9653 p-ISSN 2805-4364 VOLUME 08 ISSUE 10 OCTOBER - 2025 Page 148 of 171 Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science 1.0 Introduction Human African Trypanosomiasis (HAT), commonly known as sleeping sickness, is a vectorborne parasitic disease transmitted by tsetse flies (Glossina species) that poses a significant public health threat across sub-Saharan Africa Franco et al. (2018). The disease is caused by two subspecies of Trypanosoma brucei: T. b. gambiense, which causes chronic infection primarily in West and Central Africa, and T. b. rhodesiense, which causes acute infection in East and Southern Africa Büscher et al. (2017), Kennedy et al. (2019). HAT affects approximately 70 million people living in at-risk areas across 36 countries in sub-Saharan Africa, with an estimated 300,000 to 500,000 people currently infected W.H.O (2023). The disease progresses through two distinct stages: the hemolymphatic stage, where parasites multiply in subcutaneous tissues, blood, and lymph, and the meningo-encephalitic stage, where parasites cross the blood-brain barrier and invade the central nervous system Steverding (2008). Without proper treatment, HAT is invariably fatal, making early diagnosis and intervention critical for patient survival Malvy, and Chappuis, (2011). Despite significant progress in reducing HAT incidence through enhanced surveillance, vector control, and improved treatment protocols, the disease remains endemic in many rural communities with limited access to healthcare infrastructure Simarro et al. (2012), Pandey et al. (2015). The World Health Organization has set ambitious targets for HAT elimination as a public health problem by 2030, necessitating innovative approaches to understand transmission dynamics and optimize control strategies W.H.O (2020). Mathematical modeling serves as an essential tool for analyzing disease transmission patterns, evaluating intervention effectiveness, and guiding policy decisions in infectious disease control Heesterbeek et al. (2015), Rock et al. (2015). Traditional mathematical models using integer-order differential equations have provided valuable insights into HAT transmission dynamics but often fail to capture the complex biological processes inherent in host-vector-parasite interactions Anderson, and May (1991). These conventional models inadequately represent the memory effects, hereditary properties, and long-term dependencies that characterize real biological systems Diethelm (2010),. Fractional-order mathematical modeling has emerged as a powerful alternative that addresses these limitations by incorporating non-local characteristics and memory effects through fractional derivatives Podlubny (1999), Kilbas (2006. Fractional differential equations (FDEs) offer enhanced modeling capabilities that extend beyond classical integer-order approaches by providing a more flexible framework for investigating complex dynamical systems Baleanu et al. (2012). These models utilize fractional derivatives, such as Caputo and Riemann-Liouville operators, which possess singular kernels and excel at capturing memory effects in biological processes Caputo and Fabrizio (2015). Additionally, non-singular kernel derivatives, including Mittag-Leffler and Atangana-Baleanu operators, have gained prominence due to their superior applicability in modeling real-world phenomena Atangana, and Baleanu (2016). Recent advances in fractional calculus applications to epidemiological modeling have demonstrated significant improvements in describing disease transmission dynamics across various infectious diseases Sun et al. (2018). For instance, Atangana and Araz (2020) developed a fractional-order model for COVID-19 transmission using AtanganaBaleanu derivatives, showing enhanced prediction accuracy compared to classical models. Similarly, Baleanu et al. (2020) applied fractional calculus to analyze HIV/AIDS dynamics, demonstrating superior model flexibility and realistic behavior representation. Khan et al. (2020), investigated malaria transmission using Caputo fractional derivatives, revealing that fractional-order models better captured the complexity of host-vector interactions and longterm epidemic trends. Page No. 149 Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach Volume 08 Issue No 10 (2025) Open Access: https://gphjournal.org/index.php/as The Adams-Bashforth method has proven particularly effective for solving fractional differential equations in epidemiological applications, providing stable and accurate numerical solutions Diethelm et al. (2002) Diethelm and Ford (2004), pioneered the application of fractional Adams-Bashforth-Moulton methods for solving nonlinear fractional differential equations, establishing theoretical foundations for their implementation. Pinto and Machado (2013) utilized the Adams-Bashforth method to model fractional-order dynamics in tuberculosis transmission, demonstrating improved convergence properties and computational efficiency. More recently, Ahmed and El-Sayed (2007) applied the AdamsBashforth method to analyze hepatitis B virus dynamics using fractional calculus, showing enhanced model performance in capturing disease progression patterns. Several studies have successfully employed the Adams-Bashforth method in fractional-order disease modeling applications. Arafa et al. (2012) used this approach to investigate fractional-order HIV infection models, demonstrating superior numerical stability compared to other methods. Sweilam et al. (2007) applied the Adams-Bashforth method to solve fractional epidemic models for influenza transmission, revealing enhanced accuracy in long-term predictions. Additionally, El-Sayed et al. (2007) utilized this method to analyze fractional SIR models for measles dynamics, showing improved computational performance and solution convergence. Further research by Odibat and Shawagfeh (2007) employed the Adams-Bashforth method for solving fractional-order systems in epidemiology, emphasizing its effectiveness in handling complex nonlinear dynamics. Momani and Odibat (2007), demonstrated the method's applicability to fractional predator-prey models with epidemiological implications, while Hashim et al. (2009) applied it to fractional-order models of infectious disease outbreaks with vaccination strategies. These studies collectively highlight the AdamsBashforth method's versatility and reliability in fractional-order epidemiological modeling. The integration of fractional calculus with the Adams-Bashforth method offers significant advantages for modeling complex biological systems like HAT transmission (2010). This approach provides enhanced computational stability, improved solution accuracy, and better representation of memory effects inherent in disease transmission processes Daftardar-Gejji, and Jafari, (2006). Furthermore, fractional-order models solved using Adams-Bashforth methods demonstrate superior performance in capturing long-term dependencies and nonlocal interactions that characterize vector-borne disease dynamics Garrappa, (2018). Recent applications of fractional-order modeling to vector-borne diseases have shown promising results. Mandal et al. (2021) developed a fractional model for dengue fever transmission using Caputo derivatives and Adams-Bashforth numerical methods, revealing enhanced prediction capabilities for epidemic patterns. Similarly, Kumar et al. (2017) applied fractional calculus to chikungunya virus dynamics, employing Adams-Bashforth-Moulton methods to demonstrate improved model stability and biological realism. These studies underscore the potential of fractional-order approaches in understanding and controlling vector-borne disease transmission. The primary objectives of this study are to: (1) develop a comprehensive fractional-order mathematical model for HAT transmission incorporating both human and tsetse fly population dynamics; (2) analyze the model's mathematical properties, including existence, uniqueness, and stability of solutions; (3) implement the Adams-Bashforth method for numerical solution of the fractional differential equation system; and (4) conduct sensitivity analysis and numerical simulations to evaluate the effectiveness of various control strategies. This research addresses a significant gap in the literature by combining fractional calculus with the Adams-Bashforth method to model HAT transmission dynamics comprehensively. The study contributes to the growing body of knowledge on fractional-order epidemiological Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science modeling while providing practical insights for HAT control and elimination strategies. The manuscript is organized as follows: Section 2 presents the fractional-order model formulation, Section 3 analyzes mathematical properties and stability, Section 4 discusses numerical methods and simulation results, and Section 5 provides conclusions and recommendations for future research. Definition 1: Let ( ),fR   then the left and right Caputo fractional derivative of the function f is given by   0 ( ) ( ) m m ctt d D f t t D f t dt                     1 0 1 () 1 tm cm t D f t t f d m         The same way   ( ) ( ) m m c T t t T d D f t D f t dt                      1 1 () mTm cm TT t D f t t f d m          Definition 2: The generalized Mittag-Leffler function   , Ex  for xR is given by       ,0 , , 0 2 m m x Ex m         which can also be represented as         ,, 13 x E x xE               1 ,, 4 t S E x L t E S                   Proposition 1.1. Let   ()f R C R    and , 1 ,R m m      Therefore, the conditions given below holds: 1.     0 c tt D I f t f t   Page No. 151 Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach Volume 08 Issue No 10 (2025) Open Access: https://gphjournal.org/index.php/as 2.       00. ! k mk k t t o k t I D f t f t f t k      2.0 Model Formulation Figure 2: Schematic Diagram of the trypanosomiasis model 2.1 Model Description The rate at which individuals enter the susceptible human population is represented as H  so that T  represents the effective contact rate between susceptible individuals and infected tsetse flies. We denote T  represents the rate of re-susceptibility of recovered humans from trypanosomiasis, T  is the progression rate from T E compartment to HT I compartment. HT  is the progression rate from HT I compartment to MT I compartment. TV  transmission probability of trypanosomiasis from infected humans to susceptible tsetse flies. The natural death rate of humans is denoted as H  . Humans die due to the infectiousness of hemolymphatic trypanosomiasis at the rate HT  . The parameter HT  represents the treatment rate for humans infected with hemolymphatic trypanosomiasis, while MT  denotes the treatment rate for humans infected with meningo-encephalitic trypanosomiasis. The recovery rate from trypanosomiasis treatment is represented by T  , which transitions individuals from the treatment compartment T T to the recovered compartment T R . Disease-induced mortality occurs at different stages, with MT  representing the death rate for meningo-encephalitic trypanosomiasis and T  representing the death rate for individuals in the treatment class. For the tsetse fly population dynamics, TV  represents the recruitment rate of susceptible tsetse flies into the vector population. The natural mortality rate of tsetse flies is denoted as TV  , while TV  represents the disease-induced death rate for infected tsetse flies. The parameter Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science TV  describes the progression rate from exposed tsetse flies ( TV E ) to infected tsetse flies ( TV I ). The biting rate of tsetse flies, which determines the frequency of contact between vectors and humans, is represented by T m . The force of infection parameters play crucial roles in disease transmission dynamics. For human infection, T T TV T H mI N    represents the per capita rate at which susceptible humans acquire trypanosomiasis infection from infected tsetse flies. Conversely, for vector infection, () T TV HT MT T TV H m I I T N     represents the per capita rate at which susceptible tsetse flies become infected through contact with infected humans in various disease stages. The total human population H N serves as the normalization factor, ensuring that the force of infection appropriately scales with population density. 2.2 Model Equations The differential equations for the trypanosomiasis transmission dynamics in the human and vector population are: HH T H H H T T dS S S R dt         () TT H T H T dE SE dt       () HT T T HT HT HT H HT dI EI dt           () MT HT HT MT MT H MT dI II dt         ( ) (5) THT HT MT MT T T H T dT I I T dt           () TT T T H T dR TR dt       () TV TV TV TV TV dS S dt      () TV TV TV TV TV TV dE SE dt       () TV TV TV TV TV TV dI EI dt       Page No. 153 Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach Volume 08 Issue No 10 (2025) Open Access: https://gphjournal.org/index.php/as The force of infection for trypanosomiasis in the human population: T T TV T H mI N    The force of infection for trypanosomiasis in the tsetse fly population: () T TV HT MT T TV H m I I T N     where H H T HT MT T T N S E I I T R      is the total human population. 3.0 Fractional Trypanosomiasis mathematical model In this section, we extend the integer-order trypanosomiasis model from the differential equations by incorporating the Caputo fractional derivative operator. This modified model offers greater flexibility compared to the classical model, as the fractional-order formulation allows for varying outputs and diverse response behaviors. The fractional trypanosomiasis model is thus presented as follows: H Ct H T H H H T T DSSSR         () Ct T H T H TT SEDE       () Ct T T HT HT HT HH HT T ID E I           () Ct HT HTM TT MT MT H M D I II         ( ) (6) Ct HT HT MT M HT T T T T TD I I T           () Ct T T T H TT TRDR       () Ct TV T TVT TVV V DSS      () Ct TV TV TV TVT TVV ED S E       () Ct TV TV TV TVT TVV ID E I       Subject to positive initial conditions                   0 0 0 0 0 0 0 0 0 0 , 0 , 0 , 0 , 0 0 0 , , , 0 , 0 . H H T T HT HT MT MT T T T T TV TV TV TV TV TV S S E E I I I I T T R R S S E E I I          Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science 3.1 Positivity of model solution We considered the non-negativity of the initial values ( ) as H H N t t      Secondly, 0 if,limsup ( ) ,Nt    then our model feasible domain is given by:   9 , , , , , , , , : H T HT MT T T TV TV TV H T HT MT T T TV TV TV H H S E I I T R S E I R S E I I T R S E I                  so that 9, HR     hence,  is positively invariant. If 0 0 0 0 0 0 0 0 0 , , , , , , , , H T HT MT T T TV TV TV S E I I T R S E I are non-negative, then the solution of model (6) will be non-negative for 0t . From Eq. (6), picking the first equation, we have that CH H T H H H Tt T D S S S R         () CH H T H Tt HT D S S R         () CH T H Ht T T H D S S R         But 0 H  then ( ) 0 CH T H H Tt T D S S R        Applying the Laplace transform we obtained:   ( ) 0 CH T H Ht L D S L S               100 T H H s SH s s SH S s              10 H H s SH s S sT     By taking the inverse Laplace transform, we obtained:         ,1 0 7 H T H H S t E t S      Now since the term on the right hand side of Eq. (7) is positive, we conclude that 0 H S for 0t . In the same way, we also have that Page No. 155 Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach Volume 08 Issue No 10 (2025) Open Access: https://gphjournal.org/index.php/as 0, 0, 0, 0, 0, 0, 0, 0 T HT MT T T TV TV TV E I I T R S E I        that is are positives, therefore, the solution will remain in 9 R for all 0t with positive initial conditions. 3.2 Existence and uniqueness of our model solution Let the real non-negative be J, we consider   0,LK . The set of all continuous functions that is defined on M is represented by   0 e NL with norm as;     sup , .X K t t L Considering model (6) with initial conditions presented in (8) which can be denoted as an initial value problem (IVP) in (13).       , , 0 , ct D t Z t X t t J         0 0.XX Where                       , , , , , , , , H T HT MT T T TV TV TV Y t S t E t I t I t T t R t S t E t I t represents the classes and Z is a continuous function defined as follows;                                         1 2 3 4 5 6 7 8 9 ,() ,() ,() ,( ,, , , , , H T H H H T T HT H T H T TT T HT HT HT H HT HT HT HT MT MT H MT MT HT HT MT MT T T TV TV TV S S R Z t S t SE Z t E t EI Z t I t II Z t I t II Z t X t Z t T t Z t R t Z t S t Z t E t Z t I t                                                      ) , (8) ( ) () T T H T T T T T T TV HT MT T TV TV TV H T TV HT MT T TV TV TV H TV TV TV TV TV T TR m I I T S N m I I T E N EI                                        Using proposition (2.1), we have that,     0, H H t H T H H H T T S t S I S S R              0 ( ) , (9 ) T T t T H T H T E t E I S E        Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science Figure 2: Effect of varying T  Figure 3: Effect of varying T  on the susceptible humans on the exposed humans Figure 4: Effect of varying T  Figure 5: Effect of varying T  on the recovered humans on the infected vectors Figure 1 displays the temporal evolution of susceptible humans over a 200-day period, showing curved trajectories that initially dip below zero before rising to different equilibrium levels based on varying transmission rates ( T  ). The curves exhibit a characteristic dip-andrecovery pattern, with higher T  values (shown in red and blue) reaching higher final equilibrium states around 6 1.8 2.0 10 individuals, while lower transmission rates result in lower equilibria. This pattern reveals that higher transmission rates paradoxically lead to larger susceptible populations at equilibrium because the disease burns through the population more quickly, creating immunity that eventually allows for population recovery. The initial negative dip suggests a mathematical artifact or represents a scenario where disease pressure temporarily overwhelms recruitment, but the system ultimately stabilizes with higher transmission rates supporting larger susceptible populations due to faster cycling through the disease states. Figure 2 illustrates the dynamics of exposed humans to trypanosomiasis, showing sharp peaks that occur early in the epidemic timeline before rapidly declining to near-zero levels. The cyan line ( 0.025 T   ) exhibits the highest and earliest peak around day 20, reaching approximately 0.7 individuals per unit population, Page No. 163 Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach Volume 08 Issue No 10 (2025) Open Access: https://gphjournal.org/index.php/as while lower transmission rates show progressively smaller and later peaks. This epidemiological pattern demonstrates that higher transmission rates create more intense but shorter-lived exposure periods, as individuals rapidly progress through the exposed state into active infection. The quick decline to zero indicates that the exposed class is a transient state in the disease progression, with the timing and magnitude of peaks directly correlating with transmission intensity and determining the overall epidemic trajectory. Figure 3 presents the recovered human population dynamics, characterized by bell-shaped curves that peak around days 30-40 before gradually declining over time. All transmission rate scenarios show similar peak magnitudes (approximately 55-60 individuals), but the curves exhibit different slopes and timing, with higher T  values creating sharper, earlier peaks followed by steeper declines. This epidemiological significance reflects the temporary nature of immunity in trypanosomiasis, where recovered individuals eventually return to susceptible status through waning immunity ( T  parameter). The convergence of peak heights across different transmission rates suggests that the total number of individuals who recover is less dependent on transmission intensity than on the overall population dynamics and treatment efficacy, while the declining tails indicate continuous loss of immunity over time. Figure 4 depicts infected vector (tsetse fly) populations using a different parameter set ( TV  ), showing rapid rise-and-fall dynamics with peaks occurring around days 20-25. The magenta line ( 0.016 TV   ) demonstrates the highest peak at approximately 0.23 infected vectors per unit, while all curves rapidly approach zero by day 100. This pattern reflects the vector population's response to human infection levels, where infected vectors proliferate quickly when human cases are abundant but decline rapidly as human infections are controlled through treatment or natural recovery. The epidemiological implication is that vector control timing is critical during the early epidemic phase when vector infection rates peak, and that sustained vector populations require continuous human infection reservoirs to maintain transmission cycles. 5.0 Conclusions In this research, we formulated a fractional-order mathematical framework to comprehensively examine the transmission dynamics of trypanosomiasis and assess the efficacy of treatment-centered intervention strategies. We employed the Caputo fractional derivative, which enables the model to capture memory effects—a crucial characteristic when investigating vector-borne diseases where the current epidemiological state frequently depends not only on immediate conditions but also on the historical patterns of infection, treatment, and vector-human interactions. Acknowledging the distinctive capacity of fractional models to represent real-world disease transmission patterns with greater fidelity than conventional integer-order systems, we performed a comprehensive theoretical examination of the proposed mathematical framework. Our analysis commenced by establishing the mathematical foundations for solution existence and uniqueness, ensuring the model demonstrates consistent behavior under epidemiologically realistic conditions. To numerically solve the system of fractional differential equations, we implemented the generalized Adams-Bashforth-Moulton predictor-corrector method, a robust computational scheme specifically designed to handle the non-local characteristics inherent in fractional Yunusa, M., David, O., Egbemhenghe, J., Onuche Acheneje, G., & Atokolo, W. (2025). Numerical Methods for Addressing Fractional Order Trypanosomiasis Through the Generalized Adams-Bashforth-Moulton Approach. GPH-International Journal of Applied Science, 8(10), 148-171. https://doi.org/10.5281/zenodo.17621884 © 2025 GLOBAL PUBLICATION HOUSE | International Journal of Applied Science derivatives. Through extensive computational simulations, we investigated how different values of the fractional order parameter (as characterized by the Caputo operator) and critical epidemiological parameters, including vector biting rates, transmission coefficients, and treatment success rates across different disease stages, influence the temporal evolution of trypanosomiasis transmission within affected populations. The simulation outcomes reveal several epidemiologically significant findings. Notably, increases in vector-human contact rates and transmission probabilities correspond to substantial elevations in disease prevalence across all population compartments. Conversely, enhancing treatment rates and success probabilities for both hemolymphatic and meningo-encephalitic stages significantly reduces infection burdens throughout the community. Funding No funding was received for this research. Credit Authorship Contribution Statement Musa Yunusa: Writing – original draft, Formal analysis, Methodology. Omale David: Writing – review & editing, Validation., Joseph Egbemhenghe: Formal analysis, Methodology. Godwin Onuche Acheneje: Conceptualization, Writing – review & editing, Formal analysis. William Atokolo: Writing – review & editing, Software, Formal analysis. Declaration of Competing Interest The authors declare no financial conflicts of interest or personal relationships that could have influenced the work reported in this paper. Data Availability All parameter values and initial conditions used in this study are presented in the manuscript tables. 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