The role of asymptomatic carriers on the dynamics of a lymphatic filariasis model incorporating control strategies

This Research Article was published by the Results in Control and Optimization Volume 15, 2024This 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

Bioeconomic Model for Tilapia – Nile Perch Fishery in Polluted Environment with Constant Harvesting Efforts in Tanzanian Waters of Lake Victoria

In this paper, bioeconomic model for Tilapia (Oreochromis niloticus) – Nile perch (Lates niloticus) fishery in polluted environment with the constant harvesting efforts is developed. The model analysed to get maximum sustainable yield (MSY) points and the corresponding conditions for existence established. The equilibrium points of the model found and the conditions for their existence established. The stability analysis of the interior equilibrium point is investigated by using Jacobian matrix method. Later, numerical simulations and their corresponding graphs revealed that water pollution has significant effects on the maximum sustainable yields of both Tilapia and Nile perch produces. These effects also manifests the rapid changes of species population at the interior equilibrium point. Keywords: bioeconomic model, fishery, Tilapia, Nile perch, harvesting and water pollution

The randomness and uncertainty in dynamics of lymphatic filariasis: CTMC stochastic approach

This Research Article was published by the The European Physical Journal Plus:Volume 139, article number 162, (2024)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

Sensitivity analysis and parameters estimation for the transmission of lymphatic filariasis

This Research Article was published by the Heliyon, 2023Lymphatic 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 filariasi

Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method

This research article was published in the Results in Physics Volume 57, 2024This 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.https://doi.org/10.1016/j.rinp.2024.10736

Mathematical modeling of vehicle carbon dioxide emissions

This research article was published in the Heliyon, 2024The 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 (2) 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 2 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 2, forest biomass, and vehicle population. It is shown that increased vehicular 2 emissions have a potential contribution to the increase in atmospheric 2 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 2 dynamics

Parameters estimation, global sensitivity analysis and model fitting for the dynamics of Plutella xylostella infestations in a cabbage biomass

This research article was published by Chaos, Solitons & Fractals: X,Volume 12, 2024Plutella 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 , and 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

Fuzzy modelling on the depletion of forest biomass and forest-dependent wildlife population

A project report submitted in Franklin Open Volume 4, September 2023,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

The Significance of Stochastic CTMC Over Deterministic Model in Understanding the Dynamics of Lymphatic Filariasis With Asymptomatic Carriers

This research article was published by the Journals of Applied Mathematics ,Volume 2024, Article ID 2130429,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

Mathematical models for the dynamics of alcohol related health risks with changing behavior via cultural beliefs in Tanzania

This research article published by Communications in Mathematical Biology and Neuroscience, 2021Alcoholism 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