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We consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely $\lim _{t\to \infty } h(t)/t=\lim _{t\to \infty }[\!-g(t)/t]=c_\nu$ , with $c_\nu$ the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that $h(t)-c_\nu t$ and $g(t)+c_\nu t$ converge to some constants as $t\to \infty$ , and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild- $ N.\,lugens $ N. l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $ N.\,lugens $ N. l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $ N.\,lugens $ N. l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $ N.\,lugens $ N. l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions. [ABSTRACT FROM AUTHOR]

An intraguild predator–prey model including prey refuge and hunting cooperation is investigated in this paper. First, for the corresponding ordinary differential equation model, the existence and stability of all equilibria are given, and the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are investigated. Then, for partial differential equation model, the diffusion-driven Turing instability is obtained. What is more, the existence and non-existence of the non-constant positive steady state of the reaction–diffusion model are established by the Leray–Schauder degree theory and some priori estimates. Next, some numerical simulations are performed to support analytical results. The results showed that prey refuge can change the stability of model and even have a stabilizing effect on this model, meanwhile the hunting cooperation can make such model without diffusion unstable, but make such model with diffusion stable. Lastly, a brief conclusion is concluded in the last section. [ABSTRACT FROM AUTHOR]

The anthropogenic carbon dioxide (C O 2) emission from the burning of fossil fuels is the prime cause behind the menace of global warming. Over the past few decades, fossil fuel consumption has increased drastically to fulfill the energy demand of the growing population and economy. The population pressure has not only contributed to the increase in fossil fuel consumption but also accelerated the deforestation for industrial, agricultural, and infrastructure expansion. This paper presents a nonlinear mathematical model to study the effect of an increase in fossil fuel use and deforestation due to population pressure on atmospheric carbon dioxide concentration. Further, the effect of economic efforts applied to reduce the population pressure over the control of atmospheric C O 2 levels is explored. The model analysis shows that an increase in the fossil fuel consumption rate causes an increase in the equilibrium level of carbon dioxide. Further, it is found that an increase in the deforestation rate coefficient has a destabilizing effect on the stability of positive state of the system. If the deforestation rate crosses a critical threshold, the positive state of the system loses stability and the periodic solutions arise via Hopf-bifurcation. It is shown that at high deforestation rates, an increase in the implementation rate of economic efforts applied to reduce the population pressure may cause reduction in the amplitude of periodic oscillations. The periodic oscillations may disappear if the implementation rate of economic effort increased beyond a critical threshold and the concentration of carbon dioxide gets stabilized. [ABSTRACT FROM AUTHOR]

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM 2.5 is taken into account. The concentration response function of PM 2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P 0 of PM 2.5 and PM 2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM 2.5 by reducing the PM 2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients. [ABSTRACT FROM AUTHOR]

COVID-19 is a disease caused by infection with the virus 2019-nCoV, a single-stranded RNA virus. During the infection and transmission processes, the virus evolves and mutates rapidly, though the disease has been quickly controlled in Wuhan by 'Fangcang' hospitals. To model the virulence evolution, in this paper, we formulate a new age structured epidemic model. Under the tradeoff hypothesis, two special scenarios are used to study the virulence evolution by theoretical analysis and numerical simulations. Results show that, before 'Fangcang' hospitals, two scenarios are both consistent with the data. After 'Fangcang' hospitals, Scenario I rather than Scenario II is consistent with the data. It is concluded that the transmission pattern of COVID-19 in Wuhan obey Scenario I rather than Scenario II. Theoretical analysis show that, in Scenario I, shortening the value of L (diagnosis period) can result in an enormous selective pressure on the evolution of 2019-nCoV. [ABSTRACT FROM AUTHOR]

This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov–LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study. [ABSTRACT FROM AUTHOR]

In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper "The within-host viral kinetics of SARS-CoV-2" published in (Math. Biosci. Eng. 17(4):2853–2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number (χ 0) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection. [ABSTRACT FROM AUTHOR]

This paper considers the dynamic behaviours of a hybrid stochastic population model with impulsive perturbations. The existence of the global positive solution is studied in this paper. Moreover, under some conditions on the noises and impulsive perturbations, the properties of the persistence and extinction, stochastic permanence, global attractivity and stability in distribution are presented. Our results illustrate that impulsive perturbations play a crucial role in these properties. The bounded impulse term will not affect these properties, however, when the impulse term is unbounded, some of the properties, such as the persistence and extinction may be changed significantly. As a part of this paper, a couple of examples and numerical simulations are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

A discrete cooperative model incorporating harvesting that takes the form is proposed and studied in this paper. By using the iterative method and the comparison principle of difference equations, a set of sufficient conditions which ensure the global attractivity of the interior equilibrium of the system is obtained. Numeric simulations show the feasibility of the main result. [ABSTRACT FROM AUTHOR]

In this paper we study the exchange rate between the Euro and the US Dollar between January 3, 2003 until September 18, 2014. First we research if these exchanges follow a geometric Brownian motion, i.e. it is that future exchange rates are independent of past movements; our results are consistent with this assumption and then we make several estimates of the volatility. In the second part of the paper, we study possible periodic motions: first using discrete Fourier transform and later wavelet analysis. The techniques used are easy to understand and express, and can be implement in a transparent way by means of a few lines of code in Matlab. They can be used to understand behaviors that would seem chaotic. [ABSTRACT FROM AUTHOR]

A coupled nonlinear prey–predator system is presented. The system formulation is based on nonlinear ordinary differential equations with imprecise parameter values. In this paper, we find the equilibrium point and conduct a stability analysis of the prey–predator model using a Lyapunov functional. A comparison of our approximate analytical expressions with numerical simulation using MATLAB software is also presented. Furthermore, the proposed mathematical model is solved analytically by using the VIM and HPM for all possible parameter values in their specified ranges. Excellent agreement is noted on comparisons between the analytical and numerical results. [ABSTRACT FROM AUTHOR]

The present study develops the Clifford algebra Cl5,0 within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis — ABCD. To generate the Cl5,0 we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto the 2-, 3-, 4-vector Cl5,0 subspaces. We use a sample set of 112 5D LFVs and apply the new formula to calculate 112 32D multivectors in the Cl5,0. Next we map the 5D LFVs onto the 2-, 3-, 4-vector subspaces of the Cl5,0. In every subspace we apply a binary support vector machine to classify the mapped 112 LFVs. With the obtained results we calculate six metrics and evaluate the effectiveness of the diagnosis in every subspace. At the end of the paper we compare the classification results, obtained in every subspace, with the results obtained by the four diagnosing rules most used in clinical practice and contemporary machine learning methods. This way we reveal the potential of using Clifford algebras in the analysis and classification of medical images. [ABSTRACT FROM AUTHOR]

In this paper, we inspect the global asymptotic stability (GAS) of Ebola–epidemic using a modified Susceptible-Infected-Deceased-Pathogen (SIDP) model with perturbation. The feasible region is obtained, and we determine the basic reproduction number using the next-generation matrix method. The GAS of the disease-free and endemic equilibria are discuss and provide parameter conditions for which the stability exists. We show theoretically that the contaminated environmental Ebola human–deceased transmission model is GAS with and without probability. Numerical simulation to support our theoretical findings are presented. [ABSTRACT FROM AUTHOR]

A stochastic two-prey one-predator system with distributed delays is proposed in this paper. Firstly, applying the linear chain technique, we transform the predator–prey system with distributed delays to an equivalent system with no delays. Then, by use of the comparison method and the inequality technique, we investigate the stability in mean and extinction of species. Further, by constructing some suitable functionals, using M-matrix theory and three important lemmas, we establish sufficient conditions assuring the existence of distribution and the attractivity of solutions. Finally, some numerical simulations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected CD 4 + T cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system. [ABSTRACT FROM AUTHOR]

Explaining the mechanism of the cochlear active phonosensitive amplification has been a major problem in medicine. The basilar membrane (BM) is the key infrastructure. In 1960, Nobel Laureate von Békésy first discovered BM's traveling wave motion. Since that time, BM's models only have considered the traveling wave but not the biological activity. Therefore, a new model considering changes of BM's stiffness in space and time is established based on the immersed boundary method to describe its biological activity. It not only reproduces the results of traveling wave motion but also explains the mechanization on the generation of traveling wave. An important discovery is that changes of BM's stiffness in space and time will cause the unstable global resonance, which will induce amplification of sounds in cochlea. An important inference is that biological activity shall be included in the application of mechanical principles to the analysis of life, which is the essential difference between biomechanics and general mechanics. [ABSTRACT FROM AUTHOR]

Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, a predator-prey system with Holling type function response incorporating prey refuge is presented. By applying the analytical approaches, the dynamics behavior of the considered system is investigated, including stability, limit cycle and bifurcation. The results show that the shape of the functional response plays an important role in determining the dynamics of the system. Especially, the interesting conclusion is that the prey refuge has a destabilizing effect under some certain conditions. [ABSTRACT FROM AUTHOR]

Vertical transmissions of vector-borne diseases such as dengue virus, malaria, West Nile virus and Rift Valley fever are among challenging factors in disease control. In this paper, we used a system of differential equations to study the impacts of vertical transmission (in the vector) and horizontal (vector-to-host) transmissions cycle on the uniform persistence of a vertically transmitted disease. This is given analytically when the secondary reproduction number is greater than unity. Additional numerical results indicate that vertical transmission rates raise the epidemic level. However, we provide analytical results to reveal that vertical transmission of the disease in vectors alone without horizontal transmission, could not make the disease endemic. Furthermore, by transforming the system of differential equations to a nonlinear eigenvalue equation, the existence of a backward bifurcation is established. The directions of bifurcation is forward when the disease-induced death rate of hosts is reduced below a threshold. It is shown that the bifurcation is backward when the disease-induced death rate in the host is above a critical value. Additionally, increased disease transmission parameters also contribute to backward bifurcation. Numerical results are also provided to highlight that, depending on the initial conditions, the disease could be persistent even when the secondary reproduction number is less than unity. [ABSTRACT FROM AUTHOR]

Identifying the secondary structure of an RNA is crucial for understanding its diverse regulatory functions. This paper focuses on how to enhance target identification in a Boltzmann ensemble of structures via chemical probing data. We employ an information-theoretic approach to solve the problem, via considering a variant of the Rényi-Ulam game. Our framework is centered around the ensemble tree, a hierarchical bi-partition of the input ensemble, that is constructed by recursively querying about whether or not a base pair of maximum information entropy is contained in the target. These queries are answered via relating local with global probing data, employing the modularity in RNA secondary structures. We present that leaves of the tree are comprised of sub-samples exhibiting a distinguished structure with high probability. In particular, for a Boltzmann ensemble incorporating probing data, which is well established in the literature, the probability of our framework correctly identifying the target in the leaf is greater than 90 % . [ABSTRACT FROM AUTHOR]

A stochastic susceptible–exposed–infected–recovered (SEIR) model with nonlinear incidence rate is investigated. Under suitable conditions, existence and uniqueness of a global solution, stationary distribution with ergodicity, persistence in the mean, and extinction of the disease are obtained. Numerical simulations and conclusions are separately carried out at the end of this paper. [ABSTRACT FROM AUTHOR]

In this paper, a delayed virus model with two different transmission methods and treatments is investigated. This model is a time-delayed version of the model in (Zhang et al. in Comput. Math. Methods Med. 2015:758362, 2015). We show that the virus-free equilibrium is locally asymptotically stable if the basic reproduction number is smaller than one, and by regarding the time delay as a bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of the endemic equilibrium. Finally, we give some numerical simulations to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Differential algebra (DA) methods are currently being exploited for analyzing dynamic biosystem models for their structural identifiability (SI) properties. An early step in this approach entails finding an equivalent input–output (I/O) model. A recent approach for finding these equations, based on Grbner bases and imbedded in the app COMBOS is relatively slow and sometimes unsuccessful, even for moderate size models. In this paper, we propose a faster algorithm, using a Gaussian elimination approach for analyzing the subclass of linear dynamic biosystem models. We apply this methodology to find the simplest set of globally SI parameter combinations of these models and show that it works effectively for linear biosystem models of simple to moderate complexity. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number. [ABSTRACT FROM AUTHOR]

In this paper, we study periodic solutions for a seasonally forced SIR model with impact of media coverage. Usually, media reports, information processing, and individuals' alerted responses to the information can only arise as the number of infected individuals reaches and exceeds a certain level. The piecewise smooth righthand side is introduced to describe the impact of this kind of media coverage. Using Leray-Schauder degree theory, we establish new results on the existence of at least one positive periodic solution for a seasonally forced SIR model with impact of media coverage. Some numerical simulations are presented to illustrate the effectiveness of such media coverage. [ABSTRACT FROM AUTHOR]

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K+)-limited environment. Our both continuous and discrete models illustrate ‘cancer immunoediting’ as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Braviet al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202–206]. [ABSTRACT FROM AUTHOR]

The paper studies a periodic and delayed predator–prey system with non-monotonic functional responses and stage structure. In the system, both the predator and prey are divided into immature individuals and mature individuals by two fixed ages. It is assumed that the immature predators cannot attack preys, and the case of the mature predators attacking the immature preys is also ignored. Based on Mawhin's coincidence degree, sufficient conditions are obtained for the existence of two positive periodic solutions of the system. An example is presented to illustrate the feasibility of the main results. [ABSTRACT FROM AUTHOR]

Microbial competition for nutrients is a common phenomenon that occurs between species inhabiting the same environment. Bioreactors are often used for the study of microbial competition since the number and type of microbial species can be controlled, and the system can be isolated from other interactions that may occur between the competing species. A common type of competition is the so-called “pure and simple” competition, where the microbial populations interact in no other way except the competition for a single rate-limiting nutrient that affects their growth rates. The issue of whether pure and simple competition under time-invariant conditions can give rise to chaotic behaviour has been unresolved for decades. The third author recently showed, for the first time, that chaos can theoretically occur in these systems by analysing the dynamics of a model where both competing species grow following the biomass-dependent Contois model while the yield coefficients associated with the two species are substrate-dependent. In this paper we show that chaotic behaviour can occur in a much simpler model of pure and simple competition. We examine the case where only one species grows following the Contois model with variable yield coefficient while the other species is allowed to grow following the simple Monod model with constant yield. We show that while the static behaviour of the proposed model is quite simple, the dynamic behaviour is complex and involves period doubling culminating in chaos. The proposed model could serve as a basis to re-examine the importance of Contois kinetics in predicting complex behaviour in microbial competition. [ABSTRACT FROM AUTHOR]

Owing to its viscoelastic nature, axon exhibits a stress rate-dependent me- chanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelas- ticity is developed to illustrate the micromechanical behavior of the axon under dynamic torsional conditions. Theoretical closed-form expressions are derived to predict the de- formation, stress transfer, and failure mechanism between microtubule (MT) and tau protein while the axon is sheared dynamically. The results obtained from the present an- alytical solutions demonstrate how the MT-tau interface length, spacing between the tau proteins, and loading rate affect the mechanical properties of axon. Moreover, it is found that the MTs are more prone to rupture due to the contributions from the viscoelastic effects. Under the torsional force, the MTs are so long that the stress concentrates at the loaded end where axonal MTs will break. This MT-tau protein dynamics model can help to understand the underlying pathology and molecular mechanisms of axonal injury. Additionally, the emphasis of this paper is on the micromechanical behavior of axon, whereas this theoretical model can be equally applicable to other soft or hard tissues, owning the similar fibrous structure. [ABSTRACT FROM AUTHOR]

This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary and the stability of the solutions. [ABSTRACT FROM AUTHOR]

In this paper, based on the related theories of microbial continuous culture, fermentation dynamics, and microbial flocculant, a class of dynamic models which describe microbial flocculant with resource competition and metabolic products in wastewater treatment is proposed. By analyzing the global dynamic properties of the model, the feasibility of employing microbial metabolites as flocculant to remove harmful microorganisms is considered. [ABSTRACT FROM AUTHOR]

In this paper, we establish a unilateral diffusion Gompertz model of a single population in two patches in a theoretical way. Firstly, we prove the existence and uniqueness of an order-one periodic solution by the geometry theory of differential equations and the method of successor function. Secondly, we prove the stability of the order-one periodic solution by imitating the theory of the limit cycle of an ordinary differential equation. Finally, we verify the theoretical results by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper formulates two 3D models using stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. These models have two distinct noise sources. One is general noise whereas the other is dilution-rate-induced noise. Nonlinear Monod growth rates are assumed and the paper is mainly focused on the parameter values where coexistence is found in the deterministic model. Nondimensionalising the equations around the point of intersection of the two growth rates identifies the dimensionless substrate feed as a large parameter. This in turn is used to perform an asymptotic analysis leading to a reduced 2D system of equations describing the dynamics of the populations on and close to a line of steady states obtained previously from the deterministic stability analysis. That reduced system allows the formulation of a spatially 2D Fokker-Planck equation which, when solved numerically, admits results similar to those from the SDEs. Contrary to previous suggestions, one particular population becomes dominant at large times. Finally, we briefly explore the case where death rates are included. [ABSTRACT FROM AUTHOR]

In this paper, a predator-prey model with Holling type-I functional response and multi state impulsive feedback control is established, where the intensity of pesticide spraying and the release amount of natural enemies are linearly dependent on the given threshold in the second impulse. Firstly, the existence of order-1 periodic solution of the system is investigated by successor functions and Bendixson theorem of impulsive differential equations, then the stability of periodic solutions is proved by the analogue of the Poincaré criterion. Furthermore, in order to reduce the actual total cost and obtain the best economic benefit, the optimal economic threshold is obtained, which provides the optimal strategy for the practical application. Finally, numerical simulations for specific examples are carried out to illustrate the feasibility of the above conclusions. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model describing tuberculosis transmission with incomplete treatment and continuous age structure for latently infected and infectious individuals is investigated. It is assumed in the model that the treated individuals may enter either the latent compartment due to the remainder of Mycobacterium tuberculosis or the infectious compartment due to the treatment failure. It is shown that the global transmission dynamics of the disease is fully determined by the basic reproduction number. The asymptotic smoothness of the semi-flow generated by the system is established. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is proven that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

Microtubules (MTs) are protein filaments that provide structure to the cytoskeleton of cells and a platform for the movement of intracellular substances. The spatial organization of MTs is crucial for a cell's form and function. MTs interact with a class of proteins called motor proteins that can transport and position individual filaments, thus contributing to overall organization. In this paper, we study the mathematical properties of a coupled partial differential equation (PDE) model, introduced by Whiteet al.in 2015, that describes the motor-induced organization of MTs. The model consists of a nonlinear coupling of a hyperbolic PDE for bound motor proteins, a parabolic PDE for unbound motor proteins, and a transport equation for MT dynamics. We locally smooth the motor drift velocity in the equation for bound motor proteins. The mollification is not only critical for the analysis of the model, but also adds biological realism. We then use a Banach Fixed Point argument to show local existence and uniqueness of mild solutions. We highlight the applicability of the model by showing numerical simulations that are consistent within vitroexperiments. [ABSTRACT FROM PUBLISHER]

HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided. [ABSTRACT FROM PUBLISHER]

HIV latency remains a major obstacle to viral elimination. The activation rate of latently infected cells may depend on the age of latent infection. In this paper, we develop a model of HIV infection including age-structured latently infected cells. We mathematically analyse the model and use numerical simulations with different activation functions to show that the model can explain the persistence of low-level viremia and the latent reservoir stability in patients on therapy. Sensitivity tests suggest that the model is robust to the changes of most parameters but is sensitive to the relative magnitude of the net generation rate and the long-term activation rate of latently infected cells. To reduce the sensitivity, we extend the model to include homeostatic proliferation of latently infected cells. The new model is robust in reproducing the long-term dynamics of the virus and latently infected cells observed in patients receiving prolonged combination therapy. [ABSTRACT FROM AUTHOR]

Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves. [ABSTRACT FROM AUTHOR]

Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

A stage-structured predator-prey model (stage structure for both predator and prey) with modified Leslie-Gower and Holling-II schemes is studied in this paper. Using the iterative technique method and the fluctuation lemma, sufficient conditions which guarantee the global stability of the positive equilibrium and boundary equilibrium are obtained. Our results indicate that for a stage-structured predator-prey community, both the stage structure and the death rate of the mature species are the important factors that lead to the permanence or extinction of the system. [ABSTRACT FROM AUTHOR]