Browsing by Author "Fanuel, Ibrahim"

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Conservation of forest biomass and forest–dependent wildlife population: Uncertainty quantification of the model parameters
(Elsevier, 2023) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non–linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model
Conservation of forest biomass and forest–dependent wildlife population: Uncertainty quantification of the model parameters
(Elsevier, 2023-06) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
The ecosystem is confronted with numerous challenges as a consequence of the escalating human population and its corresponding activities. Among these challenges lies the degradation of forest biomass, which directly contributes to a reduction in forested areas and poses a significant threat to the survival of wildlife species through the intensification of intraspecific competition. In this paper, a non–linear mathematical model to study the conservation of forest and wildlife species that are reliant on forest ecosystem within the framework of human population dynamics and its related activities is developed and analysed. The study assessed the impacts of economic measures in the form of incentives on reducing population pressure on forest resources as well as the potential benefits of technological efforts to accelerate the rate of reforestation. Qualitative and quantitative analyses reveals that economic and technological factors have the potential to contribute to resource conservation efforts. However, these efforts can only be used to a limited extent, and contrary to that, the system will be destabilised. Sensitivity analysis identified the parameters pertaining to human population, human activities, economic measures, and technological efforts as the most influential factors in the model
Fuzzy modelling on the depletion of forest biomass and forest-dependent wildlife population
(Elsevier, 2023-09) Fanuel, Ibrahim; Mirau, Silas; Mayengo, Maranya; Moyo, Francis
This paper presents a system of non-linear differential equations describing the depletion of forest biomass and forest-dependent wildlife population caused by human population and its associated activities. The model incorporates the imprecise nature of the parameters, which are treated as triangular fuzzy numbers to reflect the inherent uncertainty. We utilised cut to transform these imprecise parameters into intervals. Subsequently, employing the principles of interval mathematics, we effectively converted the related differential equation into a pair of distinct differential equations. By leveraging the signed distance of the fuzzy numbers, we further simplified the equations, resulting in a single differential equation, which led to the formulation of a defuzzified model. The existence of equilibrium points with their stability behaviour is presented. Furthermore, the existence of trans-critical bifurcation is analysed. Through numerical simulations, we observe significant differences between the solutions of system in crisp and fuzzy environments. These findings highlight the importance of using fuzzy models to accurately represent the dynamics of complex natural systems. Consequently, we conclude that fuzzy models provide a trustworthy representation of the dynamics of complex natural systems.
Fuzzy modelling on the depletion of forest biomass and forest-dependent wildlife population
(Elsevier, 2023-09-01) Fanuel, Ibrahim; Mirau, Silas; Mayengo, Maranya; Moyo, Francis
This paper presents a system of non-linear differential equations describing the depletion of forest biomass and forest-dependent wildlife population caused by human population and its associated activities. The model incorporates the imprecise nature of the parameters, which are treated as triangular fuzzy numbers to reflect the inherent uncertainty. We utilised cut to transform these imprecise parameters into intervals. Subsequently, employing the principles of interval mathematics, we effectively converted the related differential equation into a pair of distinct differential equations. By leveraging the signed distance of the fuzzy numbers, we further simplified the equations, resulting in a single differential equation, which led to the formulation of a defuzzified model. The existence of equilibrium points with their stability behaviour is presented. Furthermore, the existence of trans-critical bifurcation is analysed. Through numerical simulations, we observe significant differences between the solutions of system in crisp and fuzzy environments. These findings highlight the importance of using fuzzy models to accurately represent the dynamics of complex natural systems. Consequently, we conclude that fuzzy models provide a trustworthy representation of the dynamics of complex natural systems.
Mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife population
(Springer Berlin Heidelberg, 2023-07-21) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
This paper proposes and analyses a nonlinear mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife populations using a system of differential equations. It is assumed that the growth of forest biomass, forest-dependent wildlife populations, and the human population follow logistic equations. The effect of forest biomass depletion on the survival of forest-dependent wildlife populations is investigated by introducing a function that denotes the dependence on forest biomass. The system’s behaviour near all ecologically acceptable equilibria is studied, and to confirm the analytical conclusions, a numerical simulation is performed. The model analysis shows that as forest biomass declines due to an increase in human population and its associated activities, the population of wildlife species also declines, and if no measures are taken, both forest biomass and the wildlife population may become extinct.
Mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife population
(Springer Berlin Heidelberg, 2023-07-21) Fanuel, Ibrahim; Mirau, Silas; Kajunguri, Damian; Moyo, Francis
This paper proposes and analyses a nonlinear mathematical model to study the impact of anthropogenic activities on forest biomass and forest-dependent wildlife populations using a system of differential equations. It is assumed that the growth of forest biomass, forest-dependent wildlife populations, and the human population follow logistic equations. The effect of forest biomass depletion on the survival of forest-dependent wildlife populations is investigated by introducing a function that denotes the dependence on forest biomass. The system’s behaviour near all ecologically acceptable equilibria is studied, and to confirm the analytical conclusions, a numerical simulation is performed. The model analysis shows that as forest biomass declines due to an increase in human population and its associated activities, the population of wildlife species also declines, and if no measures are taken, both forest biomass and the wildlife population may become extinct.
Mathematical modeling of refugee population dynamics and its impact on deforestation in Tanzania: An ODE-based and neural network-enhanced approach
(Elsevier, 2025-09) Kajuli, Joseph; Mayengo, Maranya; Fanuel, Ibrahim
Understanding the interplay between refugee population dynamics and environmental factors is crucial for sustainable policy planning and public health preparedness. This study integrates an ordinary differential equation (ODE)-based model with a Neural Network-Enhanced Approach to estimate key parameters governing these interactions. A system of differential equations models refugee settlement, land-use changes, and deforestation, while Physics-Informed Neural Networks (PINNs) refine parameter estimates by minimizing discrepancies between observed and predicted states. Results show that combining traditional ODE modeling with neural networks improves predictive accuracy, capturing nonlinear interactions more effectively than regression-based methods. Specifically, the study examines bifurcation behavior concerning the refugee influx rate (), deforestation rate (), and reforestation effort coefficient (). The analysis reveals that all three distributions are unimodal, peaking around 0.10 for , 0.12 for , and 0.08 for , with positive skewness indicating longer tails towards higher values. These findings underscore the urgent need for policy interventions to curb deforestation while enhancing reforestation efforts. Importantly, environmental degradation and rapid population pressures identified in the model have direct implications for public health, including increased risk of waterborne and vector-borne diseases, reduced access to clean air and food sources, and long-term mental and physical health challenges for displaced populations. Overall, this study highlights key environmental impact drivers and their health consequences, emphasizing the necessity of integrated, cross-sectoral planning in refugee-hosting regions.
Modelling the Impact of Human Population and Its Associated Pressure on Forest Biomass and Forest-Dependent Wildlife Population
(Hindawi Limited, 2023-01-12) Fanuel, Ibrahim; Kajunguri, Damian; Moyo, Francis
Mathematical models have been widely used to explain the system originating from human-nature interaction, investigate the impacts of various components, and forecast system behaviour. This paper provides a profound reference to the current state of the art regarding the application of mathematical models to study the impact of human population and population pressure on forest biomass and forest-dependent wildlife. The review focused on two aspects, namely, model formulation and model analysis. In model formulation, the review revealed that socioeconomic status influences forest resource consumption patterns, thus, stratification of the human population based on economic status is a critical phenomenon in modelling human-nature interactions; however, this component has not been featured in the reviewed models. Regarding model analysis, in most of the reviewed work, single parameter approach was utilized to perform uncertainty quantification of the model parameter; this approach has been proven to be inadequate in measuring the uncertainty and sensitivity of the parameter. Thus, the use of correlation or variance based methods, which are multidimensional parameter space methods are of significant importance. Generally, despite the limitations of many assumptions in mathematical modelling, it is revealed that mathematical models demonstrate the ability to handle complex systems originating from interactions between humans and nature.
Modelling the impacts of anthropogenic activities on forest biomass and dependent wildlife population
(NM-AIST, 2024-05) Fanuel, Ibrahim
The depletion of forest biomass and declining of forest-dependent wildlife populations are ur gent ecological and societal issues resulting from human activities such as deforestation and land-use changes. This study aims to comprehend the influence of anthropogenic activities on forest biomass and the population of wildlife dependent on forests, and to formulate appropri ate management measures. Specific objectives include forecasting forest land loss in Tanzania, analysing mathematical model describing the impact of human activities on forests and wildlife, examining the influence of fuzzy parameters on model dynamics, and evaluating the effects of economic measures and technological efforts on conservation. The study considered Tanzania where local communities heavily rely on forest resources for their livelihoods. This region also supports a rich biodiversity of wildlife species, where the forest provides essential habitats and resources for their survival. Furthermore, the study also acknowledged the existence of vari ous human activities carried out in the area which may have a significant impact on the forest ecosystem and the wildlife populations that depend on it. Four models are presented: a time series model and three dynamical system models. The key findings include: (i) The univariate time series model accurately predicts an increase in forest land loss in Tanzania with a 96.2% accuracy rate (MAPE = 0.0377), highlighting the urgency for sustainable forest management practices and conservation policies. (ii) Depletion of forest biomass due to human activities has severe implications for wildlife survival and ecological balance. Achieving this balance re quires ensuring the growth rate of forest biomass and wildlife populations exceeds their rates of utilisation and depletion, respectively. (iii) Incorporating fuzzy parameters improves model re liability by accounting for uncertainties in climate, geography, and human activities, enhancing decision-making processes. (iv) Economic measures and technological efforts have the po tential to conserve forest biomass and wildlife populations. However, careful implementation and comprehensive understanding of forest ecosystem dynamics are crucial to prevent desta bilisation. The study emphasises the need for interdisciplinary collaboration and stakeholders engagement to ensure sustainable forest use and conservation, considering the complexities and uncertainties of natural systems. Balancing forest conservation with socio-economic needs is key for the well-being of local communities and future generations.