Browsing by Author "Irunde, Jacob"

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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.
Modeling cryptosporidiosis in humans and cattle: Deterministic and stochastic approaches
(Elsevier, 2023-02-25) Luhanda, Faraja; Irunde, Jacob; Kuznetsov, Dmitry
Cryptosporidiosis is a zoonotic disease caused by Cryptosporidium. The disease poses a public and veterinary health problem worldwide. A deterministic model and its corresponding continuous time Markov chain (CTMC) stochastic model are developed and analyzed to investigate cryptosporidiosis transmission dynamics in humans and cattle. The basic reproduction number for the deterministic model and stochastic threshold for the CTMC stochastic model are computed by the next generation matrix method and multitype branching process, respectively. The normalized forward sensitivity index method is used to determine the sensitivity index for each parameter in . Per capita birth rate of cattle, the rate of cattle to acquire cryptosporidiosis infection from the environment and the rate at which infected cattle shed Cryptosporidium oocysts in the environment play an important role in the persistence of the disease whereas Cryptosporidium oocysts natural death rate, cattle recovery rate and cattle natural death rate are most negative sensitive parameters in the dynamics of cryptosporidiosis. Numerical results for CTMC stochastic model show that the likelihood of cryptosporidiosis extinction is high when it arises from an infected human. However, there is a major outbreak if cryptosporidiosis emerges either from infected cattle or from Cryptosporidium oocysts in the environment or when it emerges from all three infectious compartments. Therefore to control the disease, control measures should focus on maintaining personal and cattle farm hygiene and decontaminating the environment to destroy Cryptosporidium oocysts.
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.
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 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.