Deterministic Dynamic Model Research Articles

Stochastic models allow improved inference of microbiome interactions from time series data.

How can we figure out how the different microbes interact within microbiomes? To combine theoretical models and experimental data, we often fit a deterministic model for the mean dynamics of a system to averaged data. However, in the averaging procedure a lot of information from the data is lost-and a deterministic model may be a poor representation of a stochastic reality. Here, we develop an inference method for microbiomes based on the idea that both the experiment and the model are stochastic. Starting from a stochastic model, we derive dynamical equations not only for the average, but also for higher statistical moments of the microbial abundances. We use these equations to infer distributions of the interaction parameters that best describe the biological experimental data-improving identifiability and precision. The inferred distributions allow us to make predictions but also to distinguish between fairly certain parameters and those for which the available experimental data does not give sufficient information. Compared to related approaches, we derive expressions that also work for the relative abundance of microbes, enabling us to use conventional metagenome data, and account for cases where not a single host, but only replicate hosts, can be tracked over time.

Effectiveness and efficiency of immunisation strategies to prevent RSV among infants and older adults in Germany: a modelling study

BackgroundRecently, several novel RSV immunisation products that protect infants and older adults against RSV disease have been licensed in Europe. We estimated the effectiveness and efficiency of introducing these RSV immunisation strategies in Germany.MethodsWe used a Bayesian framework to fit a deterministic age-structured dynamic transmission model of RSV to sentinel surveillance and RSV-specific hospitalisation data in Germany from 2015 to 2019. The calibrated model was used to evaluate different RSV intervention strategies over 5 years: long-acting, single-dose monoclonal antibodies (mAbs) in high-risk infants aged 1–5 months; long-acting mAbs in all infants aged 1–5 months; seasonal vaccination of pregnant women and one-time seasonal vaccination of older adults (75 + /65 + /55 + years). We performed sensitivity analysis on vaccine uptake, seasonal vs. year-round maternal vaccination, and the effect of under-ascertainment for older adults.ResultsThe model was able to match the various RSV datasets. Replacing the current short-acting mAB for high-risk infants with long-acting mAbs prevented 1.1% of RSV-specific hospitalisations in infants per year at the same uptake. Expanding the long-acting mAB programme to all infants prevented 39.3% of infant hospitalisations per year. Maternal vaccination required a larger number to be immunised to prevent one additional hospitalisation than a long-acting mAB for the same uptake. Vaccination of adults older than 75 years at an uptake of 40% in addition to Nirsevimab in all infants prevented an additional 4.5% of all RSV hospitalisations over 5 years, with substantial uncertainty in the correction for under-ascertainment of the RSV burden.ConclusionsImmunisation has the potential to reduce the RSV disease burden in Germany.

Fire Safety Assessment of a Typical Sports Hall Building Based on Fire Dynamics and Crowd Movement Models

Fire risk analysis is one of the essential components of building design to ensure the safety of occupants and properties in case of fires. Currently, the Ministry of Public Works and Housing Regulation No. 20/PRT/M/2009 provides guidelines for conducting a fire risk analysis, however, without a clear consideration of fire dynamics in the estimation of the fire risk level. In this work, we investigate the fire safety aspects of a typical sports hall buildings by a fire dynamics deterministic model (Fire Dynamics Simulator (FDS) of the National Institute of Science and Technology, USA) and crowd movement model for occupant evacuation (Pathfinder of Thunderhead Engineering). Systematic investigations were made on the effects of the fire growth category and smoke extraction system on the Available Safe Egress Time (ASET). The results of ASET were then compared to the Required Safe Egress Time (RSET) which is obtained from the evacuation model. Our results suggest that ASET decreases exponentially with fire growth rate, especially from slow to medium growth rate. The fire growth rate significantly affects the acceptable fire risk of ASET longer than RSET. Occupant capacity, fire management systems, and smoke extraction systems play important roles in reducing fire risk. However, as the fire growth rate increases, the effects of smoke extraction in maintaining safe conditions diminish. This study provides recommendations to reduce risks to the occupants in case of fire, contributing to the considerations of the design and management of a typical sports hall building.

Cost-effectiveness of nonavalent vs bivalent HPV vaccine in Polish setting.

Human papillomavirus (HPV) is a prevalent sexually transmitted infection with significant implications for public health. In Poland, a nationwide vaccination program offers a choice between the 9-valent (9v) and 2-valent (2v) HPV vaccines. We aimed to assess the cost-effectiveness of the 9v vs 2v vaccine from the public payer perspective in Poland. A cost-effectiveness analysis was conducted to compare the public health and economic benefits of using 9v vs 2v vaccine in Poland over 100-year horizon using a previously published deterministic dynamic transmission model. A target population of girls and boys aged 12-13 years was considered. The model was populated with local epidemiological inputs, utilities, and costs, including vaccine and administration costs, as well as costs related to medical procedures for HPV-related diseases. The 9v vaccine reduced the prevalence of HPV infections and HPV-related diseases substantially more than 2v vaccine when both are compared to no vaccination strategy. The total discounted cost savings of using the 9v vaccine instead of 2v, excluding the vaccine costs, amounted to EUR 66 million. The incremental cost-effectiveness ratio amounted to 8094 EUR per quality-adjusted life year, much below the official cost-effectiveness threshold in Poland set up at the three times the annual gross domestic product per capita. 9v cost-effectiveness ratio remained unchanged when shorter time-horizons of 20, 40, 60, or 80 years were considered. Using 9v HPV vaccine in Poland is highly cost-effective compared to the 2v vaccine.

Dynamic modeling and vibration analysis for motorized spindle with uncertainties

Abstract Uncertainties inevitably exist in motorized spindle and it is difficult to accurately describe its dynamics based on a deterministic model. In this paper, a dynamic model of motorized spindle with uncertainty is proposed. The deterministic dynamic model of the motorized spindle rotor system is built by the finite element method, and the uncertainties are constructed by the polynomial chaotic expansion (PCE) method. The impact of each uncertainty parameter on the critical speed of the system is investigated by adopting the Sobol global sensitivity analysis method. The effects of uncertainties including the bearing stiffness, the material Young’s modulus, the disc mass and the unbalanced excitation on the vibration response of motorized spindle are analyzed. The modal experiments are carried out to verify the effectiveness of the model. The results show that the uncertainties have a great influence on the vibration characteristics of the motorized spindle system, in which the bearing stiffness mainly affects the high-order frequency response of the system, while the Young’s modulus affects all the order frequency response of the system. The influence of hybrid uncertainties on the frequency response of the system is more complex. This study provides a guidance to the design of motorized spindle.

Development and calibration of a mathematical model of HIV outcomes among Rwandan adults: informing equitable achievement of targets in Rwanda.

We developed and calibrated the Central Africa-International epidemiology Databases to Evaluate AIDS (CA-IeDEA) HIV policy model to inform equitable achievement of global goals, overall and across sub-populations, in Rwanda. We created a deterministic dynamic model to project adult HIV epidemic and care continuum outcomes, overall and for 25 subpopulations (age group, sex, HIV acquisition risk, urbanicity). Data came from the Rwanda cohort of CA-IeDEA, 2004-2020; Rwanda Demographic and Health Surveys, 2005, 2010, 2015; Rwanda Population-based HIV Impact Assessment, 2019; and the literature and reports. We calibrated the model to 47 targets by selecting the 50 best-fitting parameter sets among 20,000 simulations. Calibration targets reflected epidemic (HIV prevalence, incidence), global goals (percentage on antiretroviral therapy (ART) among diagnosed, percentage virally suppressed among on ART) and other (number on ART, percentage virally suppressed) indicators, overall and by sex. Best-fitting sets minimized the summed absolute value of the percentage deviation (AVPD) between model projections and calibration targets. Good model performance was mean AVPD ≤5% across the 50 best-fitting sets and/or projections within the target confidence intervals; acceptable was mean AVPD >5% and ≤15%. Across indicators, 1,841 of 2,350 (78.3%) model projections were a good or acceptable fit to calibration targets. For HIV epidemic indicators, 256 of 300 (85.3%) projections were a good fit to targets, with the model performing better for women (83.3% a good fit) than for men (71.7% a good fit). For global goals indicators, 96 of 100 (96.0%) projections were a good fit; model performance was similar for women and men. For other indicators, 653 of 950 (68.7%) projections were a good or acceptable fit. Fit was better for women than for men (percentage virally suppressed only) and when restricting targets for number on ART to 2013 and beyond. The CA-IeDEA HIV policy model fits historical data and can inform policy solutions for equitably achieving global goals to end the HIV epidemic in Rwanda. High-quality, unbiased population-based data, as well as novel approaches that account for calibration target quality, are critical to ongoing use of mathematical models for programmatic planning.

The use of an imperfect vaccination and awareness campaign in the control of antibiotic resistant gonorrhoea infection: A mathematical modelling perspective

The multi drug-resistant Neisseria gonorrhoeae has been classified by the World Health Organisation (WHO) as a high-priority global public health problem. This underlines the need for better understanding of the transmission dynamics and proposing an optimal intervention strategy to control the disease. In this article, a deterministic mathematical model for the transmission dynamics of gonorrhoea as an antibiotic resistant disease in a population with an imperfect vaccination is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection interventions to reduce antibiotic resistant cases. The threshold parameter R0, the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibits a backward bifurcation for R0<1. However, if the efficacy of the vaccine is 100% without a waning effect, the model is shown to be without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R0<1. The global sensitivity analysis of the model to variations in parameter values is also performed to determine the most influential parameters on the disease transmission. Moreover, the optimal control analysis of the full model is presented and the optimal intervention strategies are proposed. The proposed intervention strategies are shown to be able to control the disease within a relatively shorter period of time. Finally, numerical experiments are presented to support the theoretical analysis of the model.

Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure

We develop a mathematical model for the SARAS-CoV-2 double variant transmission characteristics with variant 1 vaccination to address this novel aspect of the disease. The model is theoretically examined, and adequate requirements are derived for the stability of its equilibrium points. The model includes the single variant 1 and variant 2 endemic equilibria in addition to the endemic and disease-free equilibria. Various approaches are used for the global and local stability of the model. For both strains, we determine the basic reproductive numbers R1 and R2. To investigate the occurrence of the layers (waves), we expand the model to include some analysis based on the second-order derivative. The model is then expanded to its stochastic form, and numerical outcomes are computed. For numerical purposes, we use the nonstandard finite difference method. Some error analysis is also recorded.

Modeling the Transmission Dynamics of Tuberculosis in Humans

Tuberculosis (TB) is a major threat to human health particularly in most of developing countries. In this article, we formulate and analyze a deterministic model for the transmission dynamics of pulmonary and extra-pulmonary tuberculosis. The next generation method is employed to find the basic reproduction number R0 which helps to determine whether TB clears or persists in the human population. Global stability of model equilibria is done through Lyapunov functions whereas the normalized forward sensitivity index method is adopted to determine parameters that drive tuberculosis. Analysis shows that both TB free and endemic equilibria exist. The TB free equilibrium is globally asymptotically stable whenever the basic reproduction number R0 &lt; 1 whereas the endemic equilibrium is globally asymptotically stable whenever R0 &gt; 1. Sensitivity analysis shows that the TB infection rate, the fraction of individuals who progress to pulmonary tuberculosis and its induced death drive TB. Numerical results indicate that when there are no interventions, susceptible humans decline significantly with time until when they are attracted to the steady state whereas latently infected, pulmonary and extra-pulmonary TB individuals increase until when they settle at the equilibrium states supporting the analytical results for existence of the endemic equilibrium. In light of these findings, we recommend treating humans infected with pulmonary TB who are carriers of the disease.

Causes of Backward Bifurcation in a Tuberculosis-Schistosomiasis Co-infection Dynamics

To obtain a thorough understanding of the influence of schistosomiasis infections on the transmission dynamics of tuberculosis, a deterministic mathematical model for the transmission dynamics of tuberculosis (TB) co-infection with schistosomiasis is created and examined. The aim of the research is to examine the reasons behind the backward bifurcation in the co-infection dynamics of tuberculosis and schistosomiasis. The backward bifurcation phenomena can be caused by the following parameters, according to the model's analysis (when the associated reproduction number is less than one), other than the well established route of exogeneous re-infection of latently infected TB individuals, the relative rates at which humans with latent schistosomiasis ($\eta_1$) and active schistosomiasis ($\eta_2$) are infected with TB, respectively, the lowered rate of reinfection with schistosomiasis ($\psi$), the fraction of individuals who experience fast progression to active TB ($p$), the adjustment parameter which accounts for the increased probability of infectiousness of humans with active TB and latent schistosomiasis ($\Pi_1$), the treatment rate of people infected with active TB exposed to schistosomiasis ($\zeta_{T1}$) and the rate of progression to active TB and exposed to schistosomiasis to active TB and active schistosomiasis ($\sigma$).

Mathematical modeling for the transmission dynamics of cholera with an optimal control strategy

Cholera is an acute diarrheal disease caused by Vibrio cholera, its prevalence occurs in almost all the continents of the world, annually there are about 1.3 to 4.0 million cases of cholera and 21,000 to 143,000 deaths worldwide. In this paper, we propose a deterministic model for the transmission dynamics of cholera to assess the impact of vaccines in decreasing the spread of cholera infection in Nigeria. Moreover, we develop an optimal control strategy, in which we consider personal hygiene a control strategy on infection class, with u(t) as the control function. The best values of the fitting parameters have been obtained using least square minimization to validate the model with the help of experimental data obtained from Nigeria. We perform sensitivity analysis to determine the key parameters that have impacts on the control of the spread of cholera infections in the population. In addition, the numerical simulation of the model reveals that the use of vaccines and personal hygiene will effectively control the spread of cholera infection.

Global Stability Analysis of Onchocerciasis Transmission Dynamics with Vigilant Compartment in Two Interacting Populations

A deterministic compartmental model for the transmission dynamics of onchocerciasis with vigilant compartment in two interacting populations is studied. The model is qualitatively analyzed to investigate its global asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number, R0&lt;1. When the basic reproduction number R0&gt;1, under some certain conditions on the model parameters, we prove that the endemic equilibrium is globally asymptotically stable with the aid of a suitable nonlinear Lyapunov function.

Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

COVID-19 is an infectious respiratory disease caused by a new virus, called SARS-CoV-2. Since itsinception, it has been a major cause of deaths and illnesses in the general population across the globe. Inthis paper, we have formulated and theoretically analyzed a non-linear deterministic model for COVID-19transmission dynamics by incorporating vaccination of the susceptible population. The system properties,such as the boundedness of solutions, the basic reproduction number R0, the local stability of disease-freeequilibrium(DFE), and endemic equilibrium (EE) points, are explored. Besides, the Lyapunov function isutilized to prove the global stability of both DFE and EE. The bifurcation analysis was carried out by utilizingthe center manifold theory. Then, the model is fitted with real COVID-19 cumulative data of infected casesin Kenya as from March 30, 2020, to March 30, 2022. Furthermore, sensitivity analysis was performed forthe proposed model to ascertain the relative significance of model parameters to COVID-19 transmissiondynamics. The simulations revealed that the spread of COVID-19 can be curtailed not only via vaccinationof susceptible populations but also increased administration of COVID-19 booster vaccine to the vaccinatedpersons and early detection and treatment of asymptomatic individuals.

Role of Differential Susceptibility and Infectiousness on the Dynamics of an SIRS Model for Malaria Transmission

A deterministic model for the transmission dynamics of SIRS-type malaria in hosts and SI in mosquito populations is proposed. The host population is differentiated between naive, primary, and secondary susceptible individuals. Primary and secondary infected individuals (and also recovered) are differentiated from each other according to their degree of infectiousness. The impact of changing the relative susceptibilities of primary and secondary (with respect to naive) susceptible individuals on the dynamics is investigated. Also, the impact of changing the relative infectiousness of secondary infected, primary, and secondary recovered individuals (with respect to primary infected) on the transmission dynamics of malaria is studied.

Light pollution risk rating based on linear dynamic discrete model

Nowadays, with the development of modern society, it has been more and more difficult for us to see the stars at night[1]. What shaded them? The answer is the “evil light”--light pollution. According to the study, light pollution not only harms people's physical health but also their mental health. To solve this problem[2], a model was created to classify and mark the level of light pollution in any place in the world. Its essence is a deterministic dynamic linear discrete model. This paper first studied different kinds of formula related to the treatment on soil and water. Then this paper compared the characteristics of the light pollution with them and found the differences and similarities which can improve our formula. Finally, to get a obtain a widely applicable index system, a linear weight formula was created, which is for light pollution only. Besides, created the optical intrusion formula and the average glare intensity formula. After comparing with the linear weight formula, the paper choosen the linear weight formula for its flexibility and wide use. Secondly, to make the model more accuracy, the paper selected factors that have strong impact on the light pollution. There are too many factors that can influence the light pollution, though some of them only take a little part in. The paper used the Topsis and factor analysis to find out the factors and their weights. Then this paper developed a scoring system based on the data provided by government. Finally, after searching the data for 57 protected areas, 67 rural communities, 64 suburban communities and 76 urban communities and applying them to the model and calculating, we got the final degree for each samples. And the average marks for each kind of place are0.83,0.69,0.51and0.18(preserve two decimal places). The results are very close to the reality and we used the optical imaging to help you better understand them.

Sensitivity analysis and parameters estimation for the transmission of lymphatic filariasis

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, R0 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 R0≥1. The findings reveal that rate of human infection, recruitment rate of mosquitoes increase the average new infections for Lymphatic filariasis. Moreover, asymptomatic individuals contribute significantly in the transmission of Lymphatic filariasis.

Experimental and Theoretical Brownian Dynamics Analysis of Ion Transport During Cellular Electroporation of E. coli Bacteria.

Escherichia coli bacterium is a rod-shaped organism composed of a complex double membrane structure. Knowledge of electric field driven ion transport through both membranes and the evolution of their induced permeabilization has important applications in biomedical engineering, delivery of genes and antibacterial agents. However, few studies have been conducted on Gram-negative bacteria in this regard considering the contribution of all ion types. To address this gap in knowledge, we have developed a deterministic and stochastic Brownian dynamics model to simulate in 3D space the motion of ions through pores formed in the plasma membranes of E. coli cells during electroporation. The diffusion coefficient, mobility, and translation time of Ca2+, Mg2+, Na+, K+, and Cl- ions within the pore region are estimated from the numerical model. Calculations of pore's conductance have been validated with experiments conducted at Gustave Roussy. From the simulations, it was found that the main driving force of ionic uptake during the pulse is the one due to the externally applied electric field. The results from this work provide a better understanding of ion transport during electroporation, aiding in the design of electrical pulses for maximizing ion throughput, primarily for application in cancer treatment.

Ecoepidemiological Model and Optimal Control Analysis of Tomato Yellow Leaf Curl Virus Disease in Tomato Plant

The purpose of this study is to analyze the impact of control strategies, namely, insecticide spray, roguing of a diseased tomato plant, and protective netting to protect tomato plant from tomato yellow leaf curl virus disease (TYLCVD). For this, we formulate and analyze a simple deterministic model for the transmission dynamics of TYLCVD that incorporates these control strategies. We initially take into account the constant control case, we calculate the basic reproduction number, and we investigate the existence and stability of the disease-free and endemic equilibria. We use the Kamgang-Sallet stability to ensure that the disease-free equilibrium point is globally asymptotically stable when the reproduction number R 0 is less than one. This indicates that TYLCVD dies out independent of the initial size of the tomato population. For R 0 &lt; 1 , the disease-free equilibrium becomes unstable, and the endemic equilibrium is globally asymptotically stable. This indicates that TYLCVD propagates. In the nonconstant control case, we use Pontryagin’s maximum principle to derive the necessary conditions for the optimal control of the disease. Our findings show that all the combined efforts of two out of three strategies can significantly reduce the power of infectivity of the disease except the combination of the use of insecticide spray and rouging infected tomato plants. Besides our numerical simulations show, the implementation of the combination of roguing diseased plants and protective netting has a similar effect in minimizing or eliminating TYLCV as the use of all strategies. Hence, as resources are always in scarce, we recommend policymakers to adapt the combination of the use of roguing diseased tomato plants and protective netting to eradicate the disease.

Local Stability Analysis of Onchocerciasis Transmission Dynamics With Nonlinear Incidence Functions in Two Interacting Populations

A deterministic compartmental model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is qualitatively analyzed to investigate its local asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using Routh-Hurwitz criteria, that the disease-free equilibrium is locally asymptotically stable when the associated basic reproduction number is less than the unity. When the basic reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable endemic equilibrium.

Smaller is better in competition for space.

Body size is a prominent morphological trait which affects many aspects of an organism's life. Although large body size is generally considered to be advantageous, ecologists have wondered about the benefits of being small. Many studies of body size depend on the metabolic theory of ecology since body size is an irremovable part of an organism's energy budget. Body size is also a spatial quantity and therefore is linked to spatial processes. Here, I show that competition for space leads to a benefit of being small and hence selects for increasingly smaller body size. I build a deterministic population dynamics model and a stochastic model of birth, death and dispersal in a population of individuals with two different body sizes and show that only the smaller individuals survive. I also extend the population dynamics model to continuously varying body sizes and include a stabilizing natural selection for an intermediate body size. I find that the intrinsic advantage of smaller body size in competition for space can only be overcome when natural selection for a large body size is sufficiently strong. Overall, my results point to a novel benefit of being small.