Free Equilibrium Research Articles

Synergies in renewable fuels and exhaust heat thermochemical recovery in low carbon vehicles

The impact of renewable fuels on exhaust energy recovery using catalytic thermochemical process in modern gasoline direct injection is studied with main aim of reducing vehicle carbon footprints. It is proven that supplying the engine with increased calorific value reformate would be beneficial in terms of CO2 reduction and fuel economy. In this research, the influence of butanol and ethanol on heat recovery, H2 production, and reforming efficiency are analytically and experimentally studied under various key parameters, including steam to carbon molar ratio and reactor inlet temperature under lean engine operating condition. Gibbs free energy and chemical equilibrium analyses are implemented to identify the key reaction pathways in reforming of the fuels. At lower exhaust gas temperatures where the reactions are thermodynamically limited the conversion rate is mainly controlled by the steam to carbon molar ratio and reducing fuel flow rate leads to a significant increase in fuel conversion levels. Maximum calorific value was achieved by ethanol reforming at 600 °C. However, at higher temperatures and steam to carbon molar ratios, butanol generally indicates better performance in terms of engine fuel economy, energy replacement by reformate, and CO2 reduction. These advantages are attributed to higher calorific value and higher reforming process efficiency of butanol compared to ethanol. In contrast, at lower temperatures, ethanol reforming generates more H2 as a result of highly endothermic nature of butanol steam and dry reforming reactions compared to ethanol with weaker molecular bonds and higher molecular diffusivity rate which leads to efficient use of the catalyst.

Transmission dynamic of stochastic hepatitis C model by spectral collocation method

In this research work, we present an exciting mathematical analysis of a stochastic model, using a standard incidence function, for infectious disease hepatitis C transmission dynamics. In this model, we divided the infected population into three different classes with two different infection stages known as chronic class and acute class while the third is an isolation class. We also presents briefly the Legendre spectral method for the numerical solution to the proposed model. It is observed that the disease-free equilibrium is asymptotically stable, when basic reproduction number It is also shown that the proposed model has a stable endemic equilibrium when the reproduction number Also, sensitivity analysis is carried out to study and identify the effect of parameters on R 0. Moreover, we have performed numerical simulations to study the influence of disease free equilibrium and endemic equilibrium. Legendre polynomial and Legendre weight function are used to solve the proposed stochastic system numerically. Numerical results are compared against the basic reproduction number.

Modeling the impact of early interventions on the transmission dynamics of coronavirus infection.

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ 1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

2-Hydroxy-N-m-tolyl-acetamide: Optic spectroscopy, X-ray Crystallography and DFT study

The subject of our study is 2-hydroxy-N-m-tolylacetamide (HTA), which is theoretically characterized by the amide-imidol tautomerism. The molecular and crystal structure of HTA was confirmed by X-ray diffraction analysis, and intermolecular hydrogen bonds were found in its crystal structure due to the formation of dimer form of the amide tautomer. We investigated the possibility of HTA existing in tautomeric forms using IR, UV-visible spectroscopy, as well as DFT calculations of its neutral form in the gas phase and in chloroform using the CPCM algorithm. The monomer of HTA in the amide and imidol forms was fully optimized using the DFT/6-311G(d,p) method to determine the optimal tautomeric forms and calculate the Gibbs free energies and equilibrium constants. In addition, theoretical UV and IR spectra were calculated to find key absorption bands confirming a particular tautomer. However, we were unable to capture the absorption bands responsible for the tautomeric forms in the UV and IR spectra. The stability of the amide form relative to the imidol form was determined based on the DFT calculations. The DFT calculations clearly show the existence of the amide-imidol tautomers in solution.

Mathematical model of COVID-19 in Nigeria with optimal control

The novel Coronavirus Disease 2019 (COVID-19) is a highly infectious disease caused by a new strain of severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2). In this work, we proposed a mathematical model of COVID-19. We carried out the qualitative analysis along with an epidemic indicator which is the basic reproduction number (R0) of this model, stability analysis of COVID-19 free equilibrium (CFE) and Endemic equilibrium (EE) using Lyaponuv function are considered. We extended the basic model into optimal control system by incorporating three control strategies. These are; use of face-mask and hand sanitizer along with social distancing; treatment of COVID-19 patients and active screening with testing and the third control is prevention against recurrence and reinfection of humans who have recovered from COVID-19. Daily data given by Nigeria Center for Disease Control (NCDC) in Nigeria is used for simulation of the proposed COVID-19 model to see the effects of the control measures. The biological interpretation of this findings is that, COVID-19 can be effectively managed or eliminated in Nigeria if the control measures implemented are capable of taking or sustaining the basic reproductive number R0 to a value below unity. If the three control strategies are well managed by the government namely; NCDC, Presidential Task Force (PTF) and Federal Ministry of Health (FMOH) or policymakers, then COVID-19 in Nigeria will be eradicated.

Modeling and analysis of the dynamics of HIV/AIDS with non-singular fractional and fractal-fractional operators

In the present study, we analyze the dynamics of HIV/AIDS epidemic model with fractional and the new definition of a nonlocal fractal-fractional derivative in the Atangana-Baleanu-Caputo (ABC) sense. The proposed model is initially formulated with the help of classical integer-order differential equations and then the ABC fractional derivative is used to obtain the fractional HIV/AIDS model with arbitrary order p 1. Then we present some basic properties including equilibria and the basic reproduction number of the model. The local and global stability of the fractional model at disease free equilibrium is shown and it is found that the model is stable when the threshold quantity is less than 1. Further, an efficient numerical approach is applied to present an iterative scheme for the fractional model and present graphical results for various values of p 1. After this, we make use of the new fractal-fractional operator to formulate the HIV/AIDS model in the ABC sense. The uniqueness and existence of the solutions are shown through the Picard-Lindelof theorem. Furthermore, we derive an iterative scheme of the fractal-fractional ABC model using a novel numerical method based on Adams-Bashforth fractal-fractional approachand depicts detailed graphical results for many values of fractional and fractal orders p 1 and p 2 respectively. The simulation results show that the HIV/AIDS model with the novel fractal-fractional operator provides biologically more feasible analysis than that of the classical fractional and integer-order models.

Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective.

A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity (R0 < 1), then the disease free equilibrium is stable and unstable if R0 > 1. Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

Mathematical analysis of a model for Chlamydia and Gonorrhea codynamics with optimal control

A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. Analysis of the gonorrhea-only sub-model shows the existence of a stable disease free equilibrium (DFE) and a stable endemic equilibrium (EE) when the associated reproduction number is less than one. In the absence of re-infection, the DFE of the gonorrhea-only sub-model is shown to be globally asymptotically stable when the respective reproduction number is below one. The endemic equilibrium of the gonorrhea-only sub-model is also shown to be globally asymptotically stable when reproduction is greater than one. Applying the Centre Manifold Theory, the complete model is shown to undergo backward bifurcation when the associated reproduction number is less than unity. The optimality system for the co-infection model is established using the Pontryagin’s Maximum Principle. Implementing male CT treatment and male gonorrhea treatment cause a reduction in the total number of females and males co-infected with CT and gonorrhea. Also, implementing male CT treatment and female gonorrhea treatment leads to a decrease in the total number of females and males co-infected with CT and gonorrhea. Moreover, implementing female CT treatment and male gonorrhea treatment averts the highest co-infected cases, in comparison with all the intervention strategies.

Mathematical modeling of the impact of treatment on the dynamics of typhoid

In this paper, we propose a mathematical model for the transmission of typhoid which analyzes the impact of treatment of the infected individuals on the dynamics of the disease. The model consists of human population and pathogen population. The human population is subdivided into three compartments, namely susceptible individuals, infected individuals, and recovered individuals and pathogen population comprises one compartment. We derived the basic reproduction number {mathcal {R}}_0, and analyzed the dynamical behaviors of both disease free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using MATLAB, we carried out numerical simulation and the findings indicate that effective treatment is adequate in eradicating typhoid fever.

Mathematical modeling and analysis of COVID-19 transmission dynamics in Central Java Province, Indonesia

Covid-19 is currently a pandemic that is considered as the biggest global threat that classified as the human-to-human transmissionable disease. This pandemic has affected practically all world countries. The aim of this paper is to construct a mathematical model for the spread of the Covid-19 outbreak and analyze its stability. The proposed mathematical model is STQIR (Susceptible, Traced, Quarantine, Infectious, Recovered) model. The form of the model is a nonlinear differential system with five variables. The step of the method i.e., compute the variables positifity, boundedness of solutions, and the basic reproduction number that computed using next generation matrix. Then the basic reproduction number will be used for testing the local stability of the disease free equilibrium using Routh Hurwitz criteria to examine its epidemiological relevance. This work also investigate the sensivity of the model with respect to the variation of each one of its parameters and is tested in application to the recent data on Covid-19 outbreak in Central Java Province, Indonesia.

Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point.

Global dynamics of a SEI epidemic model with immigration and generalized nonlinear incidence functional

In this paper, the global dynamics of an SEI epidemic model with constant immigration and general nonlinear incidence function is investigated. It is shown that there is neither a disease free equilibrium nor a basic reproduction number for this kind of models containing immigration terms. Moreover, the existence of a unique endemic equilibrium is proved. Using second Lyapunov method, we establish the global stability of the positive equilibrium. For a specific type of incidence function, some numerical simulations are presented to validate the theoretical results.

Lyapunov approach and global stability of Ebola virus infection model of an individual cells population

Ebola virus is among the most dangerous and devastating threats to human health, causing a large number of fatalities. In this paper, a mathematical modelling for the dynamics of Ebola virus infectious of an individual is presented as a system of nonlinear differential equations. The model has two equilibrium states namely, virus free equilibrium (VFE) and virus persistence equilibrium (VPE) states. The Effective reproduction number was obtained. The conditions under which the virus-free-equilibrium is globally asymptotically stable with the approach of linear Lyapunov function are shown when the effective reproduction numbers is less than unity. The nonlinear Lyapunov approach is employed to show the global stability of the endemic equilibrium only when the effective reproduction number is greater than unity. It was found that VFE is globally asymptotically stable if effective reproduction numbers is less than unity and VPE is globally asymptotically stable if M&lt;N, otherwise unstable if M&gt;N.

Reconciling the Experimental and Computational Hydrogen Evolution Activities of Pt(111) through DFT-Based Constrained MD Simulations

The computational hydrogen evolution activity of Pt(111) remains controversial due to apparent discrepancies with experiments concerning rate-determining activation free energies and equilibrium hydrogen coverages. A fundamental source of error may lie within the static representations of the metal–water interface commonly employed in density functional theory (DFT)-based kinetic models neglecting important entropic effects on reaction dynamics. In this work, we present a dynamic reassessment of the Volmer–Tafel hydrogen evolution pathway on Pt(111) through DFT-based constrained molecular dynamics simulations and thermodynamic integration. Hydrogen coverage effects are gauged at two distinct surface saturations, while the critical potential dependence and constant potential conditions are accounted for using a capacitive model of the electrified interface. The uncertainty in the highly nontrivial treatment of the electrode potential is carefully examined, and we provide a quantitative estimation of the error associated with dynamically simulated electrochemical barriers. The dynamic description of the electrochemical interface promotes a substantial decrease of the Tafel free energy barrier as the coverage is increased to a full monolayer. This follows from a decreased entropic barrier due to suppressed adlayer dynamics compared to the unsaturated surface, a detail easily missed by static calculations predicting notably higher barriers at the same coverage. Due to observed endergonic adsorption of active hydrogen intermediates, the Tafel step remains rate-determining irrespective of the coverage as illustrated by composed Volmer–Tafel free energy landscapes. Importantly, our explicitly dynamic approach avoids the ambiguous choice of frozen solvent configuration, decreasing the reliance on error cancellation and paving the way for less biased electrochemical simulations.

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Connectivity and rates of movement have profound effect on the persistence and extinction of infectious diseases. The emerging disease spread rapidly, due to the movement of infectious persons to some other regions, which has been witnessed in case of novel coronavirus disease 2019 (COVID-19). So, the networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. Motivated by the recent empirical evidence on the dispersal of infected individuals among the patches, we present the epidemic model SEIR (Susceptible-Exposed-Infected-Recovered) in which the population is divided into patches which form a network and the patches are connected through mean-field diffusive coupling. The corresponding unstable epidemiology classes will be synchronized and achieve stable state when the patches are coupled. Apart from synchronization and stability, the coupled model enables a range of rhythmic processes such as birhythmicity and rhythmogenesis which have not been investigated in epidemiology. The stability of Disease Free Equilibrium (or Endemic Equilibrium) is attained through cessation of oscillation mechanism namely Oscillation Death (OD) and Amplitude Death (AD). Corresponding to identical and non-identical epidemiology classes of patches, the different steady states are obtained and its transition is taking place through Hopf and transcritical bifurcation.

Modeling the effect of distancing and wearing of face masks on transmission of Covid-19 infection dynamics

The COVID-19 is an infection caused by corona virus which has been designated as pandemic in the word. In this paper, we proposed a model to study the effect of distancing and wearing of mask on transmission of Covid-19 infection dynamics. The invariant region of the model is established. The Covid-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using linearization technique method and Lyapunov method. It was found that, Covid-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R0&lt;1 and globally asymptomatically stable if R0&lt;1, otherwise unstable if R0&gt;1. More so, numerical analysis and simulations of the dynamics of the Covid-19 infection are presented. It was found that as effectiveness of face mask usage increased it resulted in a decrease in secondary cases and as physical distancing is maintained shown reduction in reproduction number. It is also found that, as infection rate increases, it translated to increase in secondary cases and as number of isolation individual increases, it decreased the reproduction number. More so, varying the treatment rate, means as treatment rate increases, it shown that an individuals in the isolation decreases.

Synthesis, characterization and thermodynamic properties of KNbO3

The potassium niobate (KNbO3) sample was hydrothermally synthesized using Nb2O5 and KOH solution as precursors. X-ray diffraction (XRD) results show that the synthesized KNbO3 is a single-phase material with an orthorhombic crystal structure and the unit cell parameters are: a = 3.9743 (2) Å; b = 5.6954 (2) Å; c = 5.7229 (2) Å; α = β = γ = 90°, V = 129.54 (1) Å3. The temperature-dependent phase transitions and enthalpy changes of KNbO3 were investigated by Differential Scanning Calorimetry (DSC) method. The heat capacity was measured experimentally by relaxation time method via physical property measurement system (PPMS, 2–300 K) and DSC sapphire method (280–820 K), respectively. The heat capacity of KNbO3 (2–300 K) was piecewise fitted into polynomials as: Cp = 3.242 × 10−1 T + 1.540 × 10−3 T3 + 1.056 × 10−4 T5-1.098 × 10−6 T7 + 2.946 × 10−9 T9 (2–10 K), Cp = 3.275 + 0.005 T + 0.044 T2-6.816 × 10−4 T3 + 4.628 × 10−5 T4-1.343 × 10−6 T5 + 1.090 × 10−8 T6 (10–50 K), Cp = 88.211 + 69.280 × 10−3 T-0.580 × 105 T−2-8.685 × 105 T2 (50–300 K). Consequently, the changes of enthalpy, entropy, Gibbs free energy and equilibrium constant were calculated based the dependence of heat capacity and temperature (280–820 K).

Mathematical model SI-SIRT of avian influenza epidemic with treatment on human

Avian influenza is a terrible respiratory infectious disease caused by the avian influenza virus. The great concern of the world’s health experts is the possibility of spreading avian influenza and becoming an uncontrollable pandemic. The study’s purpose was to derive, analyze, and interpret the mathematical model’s simulation of the avian influenza epidemic with treatment on humans. This paper constructed a mathematical model formed by SI-SIRT (Susceptible poultry, Infectious poultry, Susceptible human, Infected human, Treated human, Recovered human). We obtained a reproduction number (R0) from Analyzing the model. R0 is a formula to determine whether the disease will disappear or spread over in the future. The free disease equilibrium point was local asymptotically stable if R0 < 1, and the endemic equilibrium point was local asymptotically stable if R0 > 1.

A mathematical model to study resistance and non-resistance strains of influenza

Recently, cases of influenza virus resistance are being observed. Resistance is deadly and can cause many pandemics in future. That is why, here we investigate the situation on which the strains exist side – by – side and the difference in their mode of transmission. This paper studies two strain (resistance and non - resistance) flu model. The non-resistant strain mutates to give the resistant strain. These strains are differentiated by their incidence rates which are; bilinear and saturated for the non-resistant and saturated resistant strain respectively. This will help in studying the difference in the mode of transmission of the two strains. Equilibrium solutions are computed and Lyapunov functions are used to show their global stability. It is clear from the analysis that disease – free equilibrium is globally asymptotically stable if maxRR,RN<1. On the other hand endemic equilibrium is globally asymptotically stable if minRR,RN>1. Any strain with biggest basic reproduction ratio out performs the other. In order to support the analytic results some numerical simulations are carried out.