Search Results (6)

In this paper, a stochastic continuous-time Markov chain (CTMC) model is developed and analyzed to explore the dynamics of cholera. The multitype branching process is used to compute a stochastic threshold for the CTMC model. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity analysis methods are implemented to derive sensitivity indices of model parameters. The results show that the natural death rate $\left({\mu }_v\right)$ of a vector is the most sensitive parameter for controlling disease outbreaks. Numerical simulations indicate that the solutions of the CTMC stochastic model are relatively close to the solutions of the deterministic model. Numerical simulations estimate the probability of both disease extinction and outbreak. The probability of cholera extinction is high when it emerges from bacterial concentrations in non-contaminated/safe water in comparison to when it emerges from all infected groups. Thus, any intervention that focuses on reducing the number of infections at the beginning of a cholera outbreak is essential for reducing its transmission. Full article

Dengue fever, a mosquito-borne disease caused by the dengue virus, imposes a substantial disease burden on the world. Wolbachia not only manipulates the reproductive processes of mosquitoes through maternal inheritance and cytoplasmic incompatibility (CI) but also restrain the replication of dengue viruses within mosquitoes, becoming a novel approach for biologically combating dengue fever. A combined use of Wolbachia and insecticides may help to prevent pesky mosquito bites and dengue transmission. A model with impulsive spraying insecticide is introduced to examine the spread of Wolbachia in wild mosquitoes. We prove the stability and permanence results of periodic solutions in the system. Partial rank correlation coefficients (PRCCs) can determine the importance of the contribution of input parameters on the value of the outcome variable. PRCCs are used to analyze the influence of input parameters on the threshold condition of the population replacement strategy. We then explore the impacts of mosquito-killing rates and pulse periods on both population eradication and replacement strategies. To further investigate the effects of memory intensity on the two control strategies, we developed a Caputo fractional-order impulsive mosquito population model with integrated control measures. Simulation results show that for the low fecundity scenario of individuals, as memory intensity increases, the mosquito eradication strategy will occur at a slower speed, potentially even leading to the mosquito replacement strategy with low female numbers. For the high fecundity scenario of individuals, with increasing memory intensity, the mosquito replacement strategy will be achieved more quickly, with lower mosquito population amplitudes and overall numbers. It indicates that although memory factors are not conducive to implementing a mosquito eradication strategy, achieving the replacement strategy with a lower mosquito amount is helpful. This work will be advantageous for developing efficient integrated control strategies to curb dengue transmission. Full article

Background: Whole-genome models (GEMs) have become a versatile tool for systems biology, biotechnology, and medicine. GEMs created by automatic and semi-automatic approaches contain a lot of redundant reactions. At the same time, the nonlinearity of the model makes it difficult to evaluate the significance of the reaction for cell growth or metabolite production. Methods: We propose a new way to apply the global sensitivity analysis (GSA) to GEMs in a straightforward parallelizable fashion. Results: We have shown that Partial Rank Correlation Coefficient (PRCC) captures key steps in the metabolic network despite the network distance from the product synthesis reaction. Conclusions: FBA-PRCC is a fast, interpretable, and reliable metric to identify the sign and magnitude of the reaction contribution to various cellular functions. Full article

In this work, we replaced the integer derivative with Caputo derivative to model the transmission dynamics of measles in an epidemic situation. We began by recalling some results on the local and global stability of the measles-free equilibrium point as well as the local stability of the endemic equilibrium point. We computed the basic reproduction number of the fractional model and found that is it equal to the one in the integer model when the fractional order ν = 1. We then performed a sensitivity analysis using the global method. Indeed, we computed the partial rank correlation coefficient (PRCC) between each model parameter and the basic reproduction number R₀ as well as each variable state. We then demonstrated that the fractional model admits a unique solution and that it is globally stable using the Ulam–Hyers stability criterion. Simulations using the Adams-type predictor–corrector iterative scheme were conducted to validate our theoretical results and to see the impact of the variation of the fractional order on the quantitative disease dynamics. Full article

The purpose of this study was to evaluate the sensitivity of input parameters to output results when using the method of characteristics (MOC) for hydraulic transient simulations. Based on a gravity flow water delivery project, we selected six main parameters that affect the hydraulic transient simulation and selected maximum pressure as the output parameter in order to perform a parameter sensitivity analysis. The Morris sensitivity analysis (Morris) and the partial rank correlation coefficient method based on Latin hypercube sampling (LHS-PRCC) were both adopted. The results show that the sensitivity of each parameter is the same except for the friction factor. The flow rate and Young’s modulus are positively correlated with the maximum pressure, whereas the pipe diameter, valve closing time, and wall thickness are negatively correlated. It is discussed that the variability of the friction factor comes from the function of the flow and pressure regulating valve. When other conditions of the gravity flow project remain unchanged, the maximum pressure increases with the increase in the friction factor. The flow rate, pipe diameter, and valve closing time are the key parameters that affect the model. Meanwhile, Morris and LHS-PRCC proved to be effective methods for evaluating parameter sensitivity in hydraulic transient simulations. Full article

The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM) output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different methods of sensitivity analysis are applied in this study. The first one is the partial rank correlation coefficient (PRCC) which measures nonlinear but monotonic relationships between model inputs and outputs. The second one is based on the mutual information which provides a general measure of the strength of the non-monotonic association between two variables. Both methods are based on the Latin Hypercube Sampling (LHS) of the parameter space, and thus the same datasets can be used to obtain both measures of sensitivity. The utility of the PRCC and the mutual information analysis methods are illustrated by analyzing a complex SWMM model. The sensitivity analysis revealed that only a few key input variables are contributing significantly to the model outputs; PRCCs and mutual information are calculated and used to determine and rank the importance of these key parameters. This study shows that the partial rank correlation coefficient and mutual information analysis can be considered effective methods for assessing the sensitivity of the SWMM model to the uncertainty in its input parameters. Full article