In this paper, we investigate the dynamics of a system in which both prey and predator are harvested with constant rate. Our main objective is to find the effects of harvesting on equilibria, stability, and bifurcations in the system, which may be useful for biological management. The existence and stability of equilibrium points of the model are further investigated. A thorough qualitative analysis

Agriculture and mining get interlinked with each other when they take place concurrently in rural parts of the world. In order to explore it in mathematical terms, a nonlinear dynamical model system is proposed in this study with agricultural yield, human population and mining as system variables. The agricultural yield is assumed to have logistic growth and also, supplements rural human population

In this paper, we proposed and analyzed a nonlinear deterministic model for the impact of temperature variability on the epidemics of the malaria. The model analysis showed that all solutions of the systems are positive and bounded with initial conditions in a certain set. Thus, the model is proved to be both epidemiologically meaningful and mathematically well-posed. Using the next-generation matrix

In epidemiological modeling, the basic reproduction number is usually defined as being the spectral radius of the next-generation matrix evaluated at the trivial equilibrium. The global stability of the trivial equilibrium point was determined by the left eigenvector associated with that next-generation matrix. More recently, the fraction of susceptible individuals was also obtained from the next generation

A nonlinear SEIR model is formulated and analyzed. This model accounts for three important interventions — the saturated treatment on infective individuals, the screening on the exposed individuals and the information induced self-protection on susceptible individuals. Existence and stability of equilibria are discussed. A sensitivity analysis for the model parameters is performed and we identified

Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which

Bacterial plasmids play a fundamental role in antibiotic resistance. However, a lack of knowledge about their biology is an obstacle in fully understanding the mechanisms and properties of plasmid-mediated resistance. This has motivated investigations of real systems in vitro to analyze the transfer and replication of plasmids. In this work, we address this issue with mathematical modeling. We formulate

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability

We study a discrete-time model of host–parasitoid interactions, where the host is subject to a strong Allee effect and the parasitoid is aggregated. The system may have multiple coexisting steady states and there are two host population thresholds. The hosts become extinct if it is below the Allee threshold. The other threshold depends on the Allee threshold beyond which the host also becomes extinct

This paper concerns spatio-temporal pattern formation in a model for two competing prey populations with a common predator population whose movement is biased by direct prey-taxis mechanisms. By pattern formation, we mean the existence of stable, positive non-constant equilibrium states, or nontrivial stable time-periodic states. The taxis can be either repulsive or attractive and the population interaction

Statistical population reconstruction using age-at-harvest and catch-effort data has recently emerged as a robust and versatile approach to estimating the demographic dynamics of harvested populations of wildlife. Although most reconstruction efforts employ the multinomial likelihood approach to identify which set of model parameters best describes the observed age-at-harvest and catch-effort data

As a zoonotic disease, leptospirosis has now been identified as one of the emerging infectious diseases. In this paper, we analyze the propagation of leptospirosis and find a schedule for control programs to eradicate the disease in a cattle ranch. A mathematical model has been built with ordinary differential equations (ODEs) to understand the epidemiology of leptospirosis and main factors on its

We analyze a mathematical model for the treatment of chronic myeloid leukemia (CML). The model is designed for complete recovery of CML patients after treatment. The model developed in the paper [Bunimovich-Mendrazitsky S, Kronik N, Vainstein V, Optimization of interferon-alpha and imatinib combination therapy for CML: A modeling approach, Adv Theory Simul 2(1):1800081, 2018] introduced a combined

In this paper, a deterministic model describing the dynamics of the in-host HIV infection of CD4+ T-cells is proposed. The model incorporates the presence of the CD8+ T-cells and two types of antiretroviral drugs, for disrupting new infection and for inhibiting virus production, respectively. First, the existence, boundedness and positivity of the model solutions are shown, the basic reproduction number

We derive models of stochastic differential equations describing predator–prey interactions with cooperative hunting in predators based on a deterministic system proposed by Alves and Hilker. The deterministic model is analyzed first by providing a critical degree of cooperation below which the predators go extinct globally. Above the critical threshold, the deterministic model has two coexisting steady

For some diseases, it is recognized that immunity acquired by natural infection and vaccination subsequently wanes. As such, immunity provides temporal protection to recovered individuals from an infection. An immune period is extended owing to boosting of immunity by asymptomatic re-exposure to an infection. An individual’s immune status plays an important role in the spread of infectious diseases

We focus on the evaluation of photosynthetic organisms. Some species and tissues can endure periods of the dry season because they rely on a robust dynamics of metabolites. The metabolic dynamics are complex and challenging to address because it involves several steps, usually with hundreds of metabolites. The metabolites densities vary among species and tissues and respond to external conditions,

The importance of fear, refuge and additional food is being increasingly recognized in recent studies, but their combined effects need to be explored. In this paper, we investigate the joint effects of these three ecologically important factors in a prey–predator system with Crowly–Martin type functional response. We find that the fear of predator significantly affects the densities of prey and predator

In this paper, a model of stochastic competition between plasmid-bearing and plasmid-free organisms in a chemostat is investigated. First, we show that there is a unique global positive solution for the stochastic system. Second, by employing stochastic Lyapunov functions, Itô formula, strong law of large number and some other important inequalities, stochastic characteristics of the stochastic competition

Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles

The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study

We formulate and analyze a deterministic mathematical model for the transmission dynamics of schistosomiasis with treatment of both humans and bovines and mollu-sciciding of the contaminated environment. The model effective reproduction number is derived and analytical results show that the disease-free and endemic equilibria are both locally and globally asymptotically stable. Pontryagin’s Maximum

The aim of this paper is to investigate the dynamical behavior of a two-species predator–prey model with Holling type IV functional response and nonlinear predator harvesting. The positivity and boundedness of the solutions of the model have been established. The considered system contains three kinds of equilibrium points. Those are the trivial equilibrium point, axial equilibrium point and the interior

Water level regulates the dynamics of different populations residing in water bodies. The increase/decrease in the level of water leads to an increase/decrease in the volume of water, which influences the interactions of fishes and catching capability. We examine how seasonal variations in water level and harvesting affect the outcome of prey–predator interactions in an artificial lake. A seasonal

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between T cells and viruses. In our model, we assume that the variations in the death rate of productively infected T cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of

The spatial distribution of resources for diffusive populations can have a strong effect on population abundance. We investigate the optimal allocation of resources for a diffusive population. Population dynamics are represented by a parabolic partial differential equation with density-dependent growth and resources are represented through their space- and time-varying influence on the growth function

We present a new mathematical model to investigate the transmission dynamics of cholera under disease control measures that include education programs and water sanitation. The model incorporates the impact of education programs into the disease transmission rates and that of water sanitation into the environmental pathogen dynamics. We conduct a detailed analysis to the autonomous system of the model

The impact of human mobility on the spreading of disease in a metapopulation is emphasized on interconnecting between patches, whereas the current volume of movement within the local population is usually neglected. Here, the role of internal commuters is taken into account by two means, a local transmission rate and the volume of internal commuters. Dynamic model of human mobility in the metapopulation

Psoriasis is a chronic skin disease in which the process of hyper-proliferation (excessive division) of skin cells starts. Externally, psoriasis appears as red papules, on the surface of which there are scales of white–gray color. There is substantial evidence that T-helper cells take vital accountability for creating the hyper-proliferation of keratinocytes (skin cells), which causes itching of skin

As the two main behaviors of prey populations in ecological systems, the partially hiding behavior (PHB) and the completely hiding behavior (CHB) play a significant role in determining the dynamics of predator–prey models. This work examines to the dynamical consequences of predator–prey systems with the PHB and the CHB. Previous research has independently studied the two behaviors, and the general

We develop a dynamic model of an evolving epidemic in a spatially inhomogeneous environment We analyze the model, as a system of reaction–diffusion partial differential equations, to predict the outbreak and spatio-temporal spread of the disease The model features both an asymptomatic infectious stage and symptomatic infectious stage, with both the asymptomatic and the symptomatic infected populations

The incidence of thyroid cancer is rising all over the world, and the papillary subtype (PTC) is the primary factor for this increase. The presence of thyroid tumors is commonly associated with inc...

The Zika virus (ZIKV) epidemic is depicted to have high spatial diversity and slow growth, attributable to the dynamics of the mosquito vector and mobility of the human populations. In an effort to...

In this paper, we study the spatiotemporal dynamics of a diffusive Leslie-type predator–prey system with Beddington–DeAngelis functional response under homogeneous Neumann boundary conditions. Prel...

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant numb...

A class of deterministic predator–prey systems, where the prey population is subject to an infectious disease, is studied. The disease can be transmitted both horizontally and vertically within the...

From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios

A deterministic model for the effects on disease prevalence of the most advanced pre-erythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that cor...

Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year.1 Most of these cases and deaths are among children un...

In this paper, a mathematical model for malaria-dysentery co-infection was formulated in order to study and examine its dynamic relationship in the presence of malaria and dysentery preventive and ...

A within-human-host malaria parasite model, integrating key variables that influence parasite evolution-progression-advancement, under innate and adaptive immune responses, is analyzed. The implici...

Ebola outbreaks in Africa have occurred mostly in the Central and West Africa regions that are politically identified as the Economic Community of Central African States (ECCAS) and Economic Commun...

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop ...

A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector-host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling

We formulate an age and sex-structured deterministic model to assess the effect of increasing comprehensive knowledge of HIV/AIDS disease in the infected Adolescent Girls and Young Women (AGYW) and...

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, wer...

This study presents a new mathematical model for assessing the impact of sterile insect technology (SIT) and seasonal variation in local temperature on the population abundance of malaria mosquitoe...

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics o...

JBS formally withdraws this paper due to duplicate versions submitted to two different journals, JBS and JILSA, for publication. For details, please refer to the Retraction Notice.

Blue mussels (Mytilus edulis) are an important keystone species that have been declining in the Gulf of Maine. This could be attributed to a variety of complex factors such as indirect effects due to invasion by epibionts, which remains unexplored mathematically. Based on classical optimal foraging theory and anti-fouling defense mechanisms of mussels, we derive an ODE model for crab-mussel interactions

Malaria remains a primary parasitic disease in the tropical world, generating high morbidity and mortality in human populations. Recently, community surveys showed a high proportion of asymptomatic...

Spatial patterns through diffusion-driven instability are stationary structures that appear spontaneously upon breaking the symmetry of the spatial domain, which results only from the coupling betw...

Based on experimental results of a mouse model provided in the literature, we develop a mathematical model by using system biology approach, aiming to investigate immunotherapy for 4T1 breast cance...

This study presents a new model for the environment-host-environment transmission dynamics of V. cholerae in a community with an interconnected aquatic pond–river water network. For the case when t...

In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general ...

Most previous models for epidemic spreading are based on an assumption that all individual characteristics in a population are identical and stochastically distributed. However, in the real world, ...

In this paper, mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) with age-dependent latency and active infection. The model divides latent TB infection into two sta...