Browsing by Author "Mayengo, Maranya"

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Dynamical modeling of Salmonellosis in humans and dairy cattle with temperature and pH effects
(Elsevier Ltd., 2025-03) Trazias, Herman; Mayengo, Maranya; Irunde, Jacob; Kgosimore, Moatlhodi
Approximately 20 million cases and 0.15 million human fatalities worldwide each year are caused by Salmonellosis. A mechanistic compartmental model based on ordinary differential equations is proposed to evaluate the effects of temperature and pH on the transmission dynamics of Salmonellosis. The transmission potential of the disease in areas with temperature and pH stresses is examined. The next-generation matrix method is applied to compute the temperature-pH-dependent reproduction number . The dynamical regimes of the system are examined using Lyapunov stability theory and backward bifurcation analysis. The uncertainty and global sensitivity analysis are examined using the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) methods. The numerical simulations of the proposed model under favorable and unfavorable temperatures are performed with a confidence interval (CI) for the reliability assessment of the model parameters. The analysis shows that the ingestion rates of Salmonella enterica subsp. enterica serovar Typhimurium bacteria in humans and dairy cattle, human-to-human transmission rate, cattle-to-cattle transmission rate, human shedding rate, dairy cattle shedding rate, and the rate of producing contaminated dairy products are directly proportional to the number of infected humans and infected dairy cattle. The temperature ranges of and and pHs greater than 3.8 have a significant effect on the dynamics of Salmonellosis. In order to eliminate Salmonellosis, the study recommends treating natural water bodies using the recommended chemical disinfectants during summer seasons and in areas with temperature ranges of , cooking food at the hottest temperatures, and storing food at the lowest temperatures for all pHs.
Fuzzy Modeling for the Dynamics of Alcohol-Related Health Risks with Changing Behaviors via Cultural Beliefs
(Hindawi, 2020-07-13) Mayengo, Maranya; Kgosimore, Moatlhodi; Chakraverty, Snehashish
In this paper, we propose and analyze a fuzzy model for the health risk challenges associated with alcoholism. The fuzziness gets into the system by assuming uncertainty condition in the measure of influence of the risky individual and the additional death rate. Specifically, the fuzzy numbers are defined functions of the degree of peer influence of a susceptible individual into drinking behavior. The fuzzy basic risk reproduction number is computed by means of Next-Generation Matrix and analyzed. The analysis of reveals that health risk associated with alcoholism can be effectively controlled by raising the resistance of susceptible individuals and consequently reducing their chances of initiation of drinking behavior. When perceived respectable individuals in the communities are involved in health education campaign, the public awareness about prevailing risks increases rapidly. Consequently, a large population proportion will gain protection from initiation of drinks which would accelerate their health condition into more risky states. In a situation where peer influence is low, the health risks are likely to be reduced by natural factors that provide virtual protection from alcoholism. However, when the perceived most influential people in the community engage in alcoholism behavior, it implies an increase in the force of influence, and as such, the system will be endemic.
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 modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method
(Elsevier, 2024-01-17) Mayengo, Maranya; Mlazi, Nsulwa; Geminpeter, Lyakurwa; Kichonge, Baraka
This paper presents a numerical method for estimating four physical parameters of a single-diode circuit model based on manufacturer’s datasheet. A system of four non-linear equations are formed based on three key points of PV characteristics. The photocurrent, saturation current, ideality factor and the series resistance are solved iteratively using the proposed method. The suggested method is validated using RTC France solar cell, Chloride CHL285P and Photowatt PWP210 modules and the results are verified with respect to the in-field outdoor measurements. The proposed method shows a good agreement with the experimental data. Lastly, The model chosen is simulated under MATLB environment to assess the effects of external physical weather conditions, that is, temperature and solar irradiance. The advantage of the proposed method with respect of existing numerical techniques is that it converged faster than the widely used Newton method. Modeling of PV cell/module is essential in predicting performance of photovoltaic generators at any operating condition.
Mathematical modeling of vehicle carbon dioxide emissions
(Cell Press, 2024-01-02) Mayengo, Maranya; Donald, Pita; Lambura, Aristide
The demand for transportation, driven by an increasing global population, is continuously rising. This has led to a higher number of vehicles on the road and an increased reliance on fossil fuels. Consequently, the rise in atmospheric carbon dioxide (𝐶𝑂2) levels has contributed to global warming. Therefore, it is important to consider sustainable transportation practices to meet climate change mitigation targets. In this research paper, a non-linear mathematical model is developed to study the dynamics of atmospheric 𝐶𝑂2 concentration in relation to human population, economic activities, forest biomass, and vehicle population. The developed model is analyzed qualitatively to understand the long-term behavior of the system’s dynamics. Model parameters are fitted to actual data of world population, human economic activities, atmospheric 𝐶𝑂2, forest biomass, and vehicle population. It is shown that increased vehicular 𝐶𝑂2 emissions have a potential contribution to the increase in atmospheric 𝐶𝑂2 and the decline of human population. Numerical simulations are carried out to verify the analytical findings and we performed global sensitivity analysis to explore the impacts of different sensitive parameters on the 𝐶𝑂2 dynamics.
Mathematical models for the dynamics of alcohol related health risks with changing behavior via cultural beliefs in Tanzania
(Communications in Mathematical Biology and Neuroscience, 2021-03) Mayengo, Maranya; Kgosimore, Moatlhodi; Chakraverty, Snehashish; Seshaiyer, Padmanabhan; Caiseda, Carmen; Shirima, Gabriel
Alcoholism has continually posed health challenges in many communities for decades. In this paper, a more realistic model for health related risks associated with alcoholism is formulated. It considers a population proportion that has social cultural protection from alcohol consumption. In the context of this paper, such protection emanates from religious beliefs. The Next Generation Matrix (NGM) approach is used to compute the basic risk reproduction number. The risk free equilibrium point is proved to be globally asymptotically stable whenever the basic risk reproduction is less than unity and unstable otherwise. The sensitivity analysis of the basic risk reproduction number and numerical simulation results reveal that for effective control of the health risk problem in the community, the deliberate intervention strategies and policies should focus on discouraging alcoholic behaviors on its onset during initiation stage than focusing other population proportions already at risk.
Mathematical models for the dynamics of health related risks associated with alcoholism and its control strategy in Tanzania
(NM-AIST, 2021-08) Mayengo, Maranya
Alcoholic behavior has continually posed health challenges in many communities for decades. Referring to Tanzanian situation, this study presents a more realistic model for the dynamics of health risks associated with alcoholism. The model considered a population proportion that has social cultural protection from alcohol consumption. In the context of this study, such protec tion emanated from religious beliefs practiced in the country. Three versions of the model were analyzed considering different model analysis scenarios: the basic model, fuzzy logic model, and optimal control model. The equilibria of the basic model were obtained and their stability analysis was performed. The Next Generation Matrix (NGM) approach was used to compute the basic risk reproduction number of the basic model. The risk free equilibrium point of the ba sic model was proved to be globally asymptotically stable whenever the basic risk reproduction ratio was less than unit and unstable otherwise. The sensitivity analysis of the basic risk repro duction number of the basic model and numerical simulation were carried out. Their results revealed that deliberate intervention strategies and policies focused on discouraging alcoholic behaviors on their onset during initiation stage were more effective than dealing with alcoholic population proportions. The fuzzy logic based model analysis have confirmed this result where uncertainty conditions were assumed in the measure of influence of alcoholic individual
Modeling salmonellosis transmission dynamics in humans and dairy cattle with optimal controls
(Elsevier, 2025-02) Trazias, Herman; Irunde, Jacob; Kgosimore, Moatlhodi; Mayengo, Maranya
In this paper, we develop a mathematical model to examine the transmission dynamics and control analysis of salmonellosis in humans and dairy cattle. The model considers three time-dependent controls (improving hygiene, vaccination, and organic acid disinfectants), human and dairy cattle populations, and Salmonella typhimurium bacteria in the environments and dairy products. The next generation matrix technique is applied to compute the effective reproduction number that gauges the persistence and extinction of salmonellosis while adopting the proposed control interventions. The stability behavior of the equilibrium states is examined using the Lypunov function method based on the effective reproduction number . The Latin hypercube sampling and the partial rank correlation coefficient methods are used to investigate the sensitivity and uncertainty of input parameters against model outputs. The results indicate that improving hygiene and vaccination can eliminate salmonellosis. Improving hygiene habits at a rate of at least 0.9 per day is recommended to eliminate salmonellosis. An efficacious vaccine that can immunize at least 85% of the vaccinated dairy cattle is also recommended to eradicate salmonellosis if it can be implemented to vaccinate susceptible dairy cattle at a rate of at least 0.45 per day for the first 30 days of the salmonellosis outbreak. The use of all three controls is recommended to eliminate salmonellosis quickly and at the lowest cost.
Modeling the dynamics of Diamondback Moth infestations on cabbage biomass
(ELSEVIER, 2023-01-01) Paul, Daniel; Mayengo, Maranya; Daudi, Salamida
The Diamondback Moth (Plutella xylostella) is a notorious agricultural pest that poses significant challenges to cabbage production. In this study, we formulated and analyzed the deterministic differential equations to capture the infestations dynamics of diamondback moth in a cabbages biomass, taking into account the use of environmentally friendly pesticides. To study its dynamics we computed the threshold number, , based on the pest-free equilibrium point. The results indicate that when , the equilibrium point is both locally and globally stable. Conversely, when , the coexistence point becomes globally asymptotically stable. The stability of the equilibrium points were both Locally and globally assessed using Ruth Hurwitz’s criteria for local stability and Lyapunov functions for global analysis. A comprehensive numerical analysis was conducted, confirming the substantial support for the analytical findings. Finally, this research suggests that in order to reduce the impact of the diamondback moth, it is necessary to decrease the threshold value smaller than a unity through the adoption of effective inter-cropping techniques and the use of environmentally friendly pesticides.
Modeling the influence of fear and patients’ attitudes on the transmission dynamics of tuberculosis
(Springer Nature, 2025-01-08) Ruoja, Chiganga; Mayengo, Maranya; Nyerere, Nkuba; Nyabadza, Farai
In this study we discussed the ongoing global health challenge of tuberculosis (TB), which is caused by the Mycobacterium tuberculosis bacteria. While in several studies, the transmission dynamics of TB were examined, it is noted in this work that the impacts of social processes like disease-induced fear and patient attitudes toward hospital treatment have been receiving a poor discussion on understanding the disease transmission and its control. In this paper we present and discuss a deterministic mathematical model to investigate how these social processes influence the transmission dynamics of TB. The basic reproduction number is calculated and used to examine the stability of steady states. Additionally, we conducted a sensitivity analysis which tells what are the parameters that most significantly affect . The key findings from the analytical and numerical simulations indicate that high levels of disease-induced fear in the population, coupled with positive attitudes toward hospital treatment, can significantly reduce TB prevalence. Based on these results, the study recommends implementing control programs that address these social processes as part of the ongoing efforts to combat the TB burden.
Parameters estimation, global sensitivity analysis and model fitting for the dynamics of Plutella xylostella infestations in a cabbage biomass
(Elsevier, 2024-01-24) Mayengo, Maranya; Daniel, Paul; Salamida, Daudi
Plutella xylostella, commonly called Diamondback moth (DBM), a highly destructive and rapidly spreading agricultural pest originally from Europe. This pest poses a significant threat to global food security, with estimates suggesting that periodic outbreaks of Diamondback moth lead to annual crop losses of up to $US 4 − 5 billion worldwide. Given the potential for such substantial losses, it is crucial to employ various methods and techniques to understand the factors affecting the interaction between Diamondback moths and cabbage plants, which, in turn, impact cabbage biomass. In this paper, we propose a deterministic ecological model to capture the dynamics of Plutella xylostella infestations in cabbage biomass. The model is designed based on the life cycle stages of the pest, aiming at targeting the specific stage effectively. The synthetic data is generated using Least Square Algorithm through addition of Gaussian noise into numerically obtained values from existing literature to simulate real-world data. Global sensitivity analysis was done through Latin Hypercube sampling, highlights the significance of parameters such as 𝜓, 𝛼𝐸 and 𝛿 positively influence the growth of the diamondback moth in a cabbage biomass. In light of these findings, the study proposes that control strategies should be specifically directed towards these sensitive parameters. By doing so, we mitigate the pest population and enhance cabbage production.
Predatory effects on the dynamics of Spodoptera Frugiperda infestations in maize
(ELSEVIER, 2023) Reuben, Yusuph; Mayengo, Maranya; Daudi, Salamida
Maize remains in demand due to its nutritive value, capacity to provide food for a growing world population, contribution to food security, and increase in worldwide investments in ethanol as a biofuel. However, the invasion and widespread infestation of Spodoptera frugiperda result in significant maize yield losses, leading to a lower standard of living and a weakened economy for maize producers. This study builds differentiable equations to simulate the behavior of the Spodoptera frugiperda-maize biomass model, incorporating predators and best farming practices. The model exhibits six points of equilibrium, all of which are locally asymptotically stable if the necessary requirements are met. Latin Hypercube Sampling (LHS) and PRCC multivariate analysis were employed to identify the sensitive parameters affecting the pest. Numerical simulations suggest that, in the early stages, integrating natural enemies with best farming practices proves to be an effective intervention as it directly reduces the pest population and promotes sustainable pest control.
The randomness and uncertainty in dynamics of lymphatic filariasis: CTMC stochastic approach
(EPJ PLUS - Condensed Matter and Complex Systems, 2024-02-15) Stephano, Mussa A.; Irunde, Jacob; Mayengo, Maranya
Lymphatic filariasis represents the primary cause of long-term, permanent disability, and dysfunction in the human immune system. In this study, we have devised and assessed deterministic and continuous-time Markov chain (CTMC) stochastic models to gain insights into the dynamics of lymphatic filariasis and approximate the probabilities of disease extinction or outbreak. The CTMC stochastic model is an adapted version of the existing deterministic model that accounts for uncertainties and variations in disease transmission dynamics. The findings from the deterministic model indicate that disease extinction is possible when , while an outbreak is likely when . Further examination of the deterministic model emphasizes the significant role of asymptomatic individuals in the transmission of lymphatic filariasis. To estimate the probabilities of disease extinction or outbreak, we employed multitype branching processes and numerical simulations. The results demonstrate that lymphatic filariasis outbreaks are more probable when microfilariae parasites are introduced by exposed humans, asymptomatic humans, acutely infected humans, exposed mosquitoes, or infectious mosquitoes. Conversely, the disease is more likely to be eradicated if it originates from chronically infected humans. Utilizing stochastic methods provides a more authentic portrayal of how lymphatic filariasis spreads, granting a better understanding of the spectrum of potential results and their related probabilities. Therefore, stochastic CTMC models become indispensable for generating reliable forecasts and well-informed choices in situations where deterministic models might oversimplify or inaccurately depict the inherent unpredictability.
The role of asymptomatic carriers on the dynamics of a lymphatic filariasis model incorporating control strategies
(ELSEVIER, 2024-05-03) Stephano, Mussa; Mayengo, Maranya; Irunde, Jacob
This study presents a mathematical model to investigate the patterns of transmission in lymphatic filariasis. The model considers chronic, acute, and asymptomatic individuals and integrates key control strategies. Random synthetic data is generated robustly through numerical solutions to closely replicate real-world scenarios and encompass uncertainties. The synthetic data adheres to a Gaussian distribution to ensure validity and reliability. Following the derivation of the basic and effective reproduction number using the next generation matrix approach, Latin Hypercube Sampling (LHS) and the Partial Rank Correlation Coefficient (PRCC) algorithm is utilized to assess the parameters that significantly influence the model outputs. The study examine the trajectories of different population compartments through numerical simulations over time, with particular emphasis on the role played by asymptomatic individuals in the transmission of the disease. To assess the potential for disease elimination, the study introduces a range of strategies involving protective measures, treatment interventions, and mosquito control. These strategies are determined through sensitivity analysis. The findings demonstrate that the simultaneous implementation of all control measures has a noteworthy effect in managing lymphatic filariasis. In conclusion, the proposed model enhances understanding of lymphatic filariasis dynamics and informs effective control strategies.
Sensitivity analysis and parameter estimation for evaluating the impact of water pollution on aquatic species
(Computational Ecology and Software, 2025-05-21) Ngalya, Christopher; Mirau, Silas; Mayengo, Maranya
Aquatic ecosystems are highly sensitive to changes in environmental conditions, making it essential to identify the key factors that influence the dynamics of species populations. This study introduced a nonlinear mathematical model, analyzed it, and identified key sensitive parameters that were used in assessing the impact of water pollution on aquatic ecosystems. Global sensitivity analysis was conducted to determine the parameters significantly impacting aquatic species populations. Parameters were estimated using the least squares method, while sensitivity analysis was performed via Partial Rank Correlation Coefficient (PRCC) and Latin Hypercube Sampling (LHS). Parameters related to organic pollutant growth rates, pollutant absorption rates, and oxygen penetration were identified as positively affecting aquatic species populations by enhancing nutrient availability and metabolic activity. Conversely, competition and inorganic pollutant discharge were found to impact aquatic populations negatively. These findings highlight the critical role of managing sensitive parameters such as pollutants and competitive interactions to maintain and improve the health of aquatic ecosystems.
Sensitivity analysis and parameters estimation for the transmission of lymphatic filariasis
(Heliyon, 2023-05-16) . Stephano, Mussa; Mayengo, Maranya; Irunde, Jacob; Kuznetsov, Dmitry
Lymphatic filariasis is a neglected tropical disease which poses public health concern and socio- economic challenges in developing and low-income countries. In this paper, we formulate a deterministic mathematical model for transmission dynamics of lymphatic filariasis to generate data by white noise and use least square method to estimate parameter values. The validity of estimated parameter values is tested by Gaussian distribution method. The residuals of model outputs are normally distributed and hence can be used to study the dynamics of Lymphatic filariasis. After deriving the basic reproduction number, 0 by the next generation matrix approach, the Partial Rank Correlation Coefficient is employed to explore which parameters significantly affect and most influential to the model outputs. The analysis for equilibrium states shows that the Lymphatic free equilibrium is globally asymptotically stable when the basic reproduction number is less a unity and endemic equilibrium is globally asymptotically stable when 0 ≥ 1. The findings reveal that rate of human infection, recruitment rate of mosquitoes increase the average new infections for Lymphatic filariasis. Moreover, asymptomatic individual contribute significantly in the transmission of Lymphatic filariasis
The Significance of Stochastic CTMC Over Deterministic Model in Understanding the Dynamics of Lymphatic Filariasis With Asymptomatic Carriers
(Hindawi, 2024-05-04) Stephano, Mussa; Irunde, Jacob; Mayengo, Maranya; Kuznetsov, Dmitry
Lymphatic filariasis is a leading cause of chronic and irreversible damage to human immunity. This paper presents deterministic and continuous-time Markov chain (CTMC) stochastic models regarding lymphatic filariasis dynamics. To account for randomness and uncertainties in dynamics, the CTMC model was formulated based on deterministic model possible events. A deterministic model’s outputs suggest that disease extinction is feasible when the secondary threshold infection number is below one, while persistence becomes likely when the opposite holds true. Furthermore, the significant contribution of asymptomatic carriers was identified. Results indicate that persistence is more likely to occur when the infection results from asymptomatic, acutely infected, or infectious mosquitoes. Consequently, the CTMC stochastic model is essential in capturing variabilities, randomness, associated probabilities, and validity across different scales, whereas oversimplification and unpredictability of inherent may not be featured in a deterministic model.
The Volterra–Lyapunov matrix theory for global stability analysis of alcohol-related health risks model
(Elsevier, 2023-01) Mayengo, Maranya
This paper studies the global stability analysis of a modified framework proposed by Mayengo et al. on alcohol-related health risks model. We first present the global stability analysis of risk-free equilibrium (RFE). Later, the global stability of the risk endemic equilibrium is studied. This goal was achieved by appropriate utilization of the symmetrical properties in the structure of Volterra–Lyapunov matrices. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in alcohol-related health risks and similar models. The numerical examples are simulated to validate the theoretical model results presented.