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

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

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

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

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 number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters

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 increased levels of cytokines, such as interleukin 6 (IL-6). Considering PTC patients treated with thyroidectomy and radioactive iodine 131I (RAI), we propose an ordinary differential system using four variables:

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 understand the transmission dynamics of Zika virus, we formulate a new compartmental epidemic model with a system of seven differential equations and 11 parameters incorporating the decaying transmission

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 host population but cannot be spread between the two trophic levels. Using the mathematical tools of uniform persistence, we derive sufficient conditions for which the interacting populations can coexist

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. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equations is presented. For the diffusive model, firstly, it is shown

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 and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction

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 implicit role of immunity on the steady state parasite loads and parasitemia reproduction number (ℛ0), a threshold parameter measuring the parasite’s annexing ability of healthy red blood cells (HRBCs), eventually

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 Community of Western African States (ECOWAS), respectively. In the ECOWAS region, people and goods are allowed to travel freely across national borders of all the 15 member countries, but in the ECCAS region such

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 treatment measures. First, analysis of the single infection steady states was done and then the basic reproduction number was obtained. Furthermore, investigation into the existence and stability of equilibria

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 correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector–host models;

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 under five. The main control method in malaria endemic regions has been through the use of insecticide-treated nets (ITNs). Although this approach has been fairly successful, the gains are threatened by mosquito-resistance

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, Adolescent Boys and Young Men (ABYM) populations in Kenya. Mathematical analysis of infection through sub-network analysis was carried out to trace various infection routes and the veracity of various transmission

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, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the

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 mosquitoes in an endemic setting. Simulations of the model, using temperature data from Kipsamoite area of Kenya, show that a peak abundance of the mosquito population is attained in the Kipsamoite area when the mean

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 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 (OFT) and anti-fouling defense mechanisms of mussels, we derive an ODE model for crab–mussel interactions

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 of the prey–predator model where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The considered population model has

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 cases, which are characterized by a low parasitemia and a lack of malaria symptoms. Until now, the asymptomatic population is not treated for malaria and thus remains infective for a long time. In this paper

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 between the reaction and the diffusion processes. This paper is concerned with a modified Leslie–Gower-type model with cross-diffusion and indirect predation effect. We first prove the global existence, non-negativity

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 cancer. It is worth to mention that only 4 types of cells (tumor cells, CD8+ T cells, regular T cells (Tregs), and tumoricidal myeloid CD11b+Gr1dim cells) are quantitatively measured in experiments, which make

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 the human host is the sole target of anti-cholera control and the volume of water in the pond is maximum, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever a

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 nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two

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, individuals have different behavioral characteristics for resisting infections, one of which is self-protective behavior. In this study, we suggest an equation describing self-protective behavior and use

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 stages: an early stage of high risk of developing active TB and a late stage of lower risk for developing active TB. Infected persons initially progress through the early latent TB stage and then can either

Prediction of least energy conformation of a protein from its primary structure (chain of amino acids) is an optimization problem associated with a large complex energy landscape. In this study, a simple 2D hydrophobic–hydrophilic model was used to model the protein sequence, which allows the fast and efficient design of genetic algorithm-based protein structure prediction approach. The neighborhood

The progressive and increasing invasion of an opportunistic predator, the lionfish (Pterois volitans) has become a major threat for the delicate coral-reef ecosystem. The herbivore fish populations, in particular of Parrotfish, are taking the consequences of the lionfish invasion and then their control function on macro-algae growth is threatened. In this paper, we developed and analyzed a stage-structured

Vaccination is among the most effective means of preventing and controlling infectious disease outbreaks. Mathematical models can be used to identify the optimal allocation of vaccine among various groups when host populations are heterogeneous. Population heterogeneity may affect individual decision-making and government policy. We show that mixing among sub-populations can profoundly influence the

Gene regulation is fundamental for cell survival. This regulation must be both robust to noise and sensitive enough to external stimuli to elicit the proper responses. In this work, we study, through stochastic numerical simulations, how a gene regulatory network with a positive feedback loop responds to environmental changes in the presence of intrinsic and extrinsic noises. Noise effects were characterized

The Notch–Delta signaling pathway is a highly conserved signaling system that partakes in a diverse process of growth, patterns and differentiation. Experiments have shown that Delta from different cells activates this pathway (trans-activation) while Delta from the same cell inhibits this pathway (cis-inhibition). The Notch–Delta interactions could switch a cell to one of the two opposite fates: either

This paper deals with the computational modeling of the bioluminescence pattern formation in suspensions of Escherichiacoli bacteria. The aim was to develop a computational model for simulating the bacterial populations consisting of two subpopulations of active and passive cells. A suitable model based on Keller–Segel and Fisher equations was proposed and the spatiotemporal patterns were simulated

Recently, pest control has become a very interesting research topic because it is closely associated with agricultural and economic loss. Empirical evidence shows that pest insects are responsible for lower crop production and many other adverse effects on the farming sector. There are several biological, physical and chemical control mechanisms. However, the biological control of pest populations

Considering that environmental factors, diet, subconscious mind and other uncertainties play an important role in the process of delaying and treating diseases, we propose, in this paper, an amended Hepatitis B virus (HBV) model with stochastic perturbation, and investigate the longtime dynamics of this stochastic model. First, if the basic reproductive number of the corresponding deterministic model

Cholera is a water-borne disease and a major threat to human society affecting about 3–5 million people annually. A considerable number of research works have already been done to understand the disease transmission route and preventive measures in spatial or non-spatial scale. However, how the control strategies are to be linked up with the human migration in different locations in a country are not

We report a mathematical model depicting gliomas and immune system interactions by considering the role of immunotherapeutic drug T11 target structure (T11TS). The mathematical model comprises a system of coupled nonlinear ordinary differential equations involving glioma cells, macrophages, activated cytotoxic T-lymphocytes (CTLs), immunosuppressive cytokine transforming growth factor-β (TGF-β), immunostimulatory

We study the interspecies competition in a simple resource–consumer model which includes the resource supply as a dynamic variable. In the model, an organism of each species needs to consume a certain minimum rate of resource (food) to survive; a higher rate of consumption is required for reproduction. We analyze the orbit diagrams and Lyapunov exponents in order to characterize the system dynamical

This study is concerned with harvesting a renewable resource that is surviving in a polluted environment. Fall in the revenue from the resource due to presence of pollution in the environment drives the sole owner to allocate a part of the available effort towards treating the environment and the interest is to find the optimal allocation of the available effort towards harvesting the resource and

Deoxyribonucleic Acid (DNA) sequencing has become indispensable to the modern biological and medicine sciences. DNA fragmentation is a preliminary step in a dominant technique called shotgun sequencing that provides a time and cost effective strategy for the DNA sequencing. In this paper, we propose a probabilistic model for the random DNA fragmentation and derive an average number of fragments with

In this paper, we present a new method for developing a class of nested multiscale models for directly transmitted infectious disease systems that integrates within-host scale and between-host scale using community pathogen load (CPL) as a new public health measure of a community’s level of infectiousness and as an indicator of the effectiveness of health interventions. The approach develops a multiscale

Aphids, the sap-sucking insects, often feeding in clusters on new plant growth, have resulted in large amounts of resources and efforts being spent attempting to control their activities. Taking cotton aphids as an example, this paper presents optimal control problems governed by stochastic models with impulsive interferences. Differing from the moment closure equation methods which are computationally

Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping

Protein–protein interaction (PPI) is very important for various biological processes and has given rise to a series of prediction-computing methods. In spite of different computing methods in relation to PPI prediction, PPI network projects fail to perform on a large scale. Aiming at ensuring that PPI can be predicted effectively, we used a deep neural network (DNN) for the study of PPI prediction

In this work we formulate a mathematical model to assess the importance of sexual transmission during the Zika virus outbreak that occurred in Rio de Janeiro, Brazil, in 2015. To this end, we deduce from the model an analytical expression of the basic reproduction number of Zika, R0, in terms of the vectorial and sexual transmissions, and we use the estimations given in Ref. 1 [Villela DAM, Bastos

In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable

Electricigens can transfer electrons that produced in intracellular metabolic processes to cellular surface to restore extracellular insoluble electron acceptors (extracellular electron transfer, EET). To uncover the molecular mechanisms underlying EET processes, we integrated transcriptome changes accompanying such processes with molecular network. Firstly, time-series expression datasets for Shewanella

In this paper, we have investigated a spatial predator–prey model with hunting cooperation in predators. Using linear stability analysis, we obtain the condition for diffusive instability and identify the corresponding domain in the space of controlling parameters. Using extensive numerical simulations, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing

Successful immunologic control of HIV infection can be achieved in long-term non-progressors or HIV-1 controllers. Dendritic cells (DCs) are required for specific antigen presentation to naïve T lymphocytes and for antiviral, type I interferon secretion. To understand this mechanism, we develop a mathematical model that describes the role of direct presentation (replicating virus-infected DCs or other

In this paper, we propose a mathematical model to evaluate the transmission of Tuberculosis with drug-resistant strains and with drug-sensitive strains. Based on the epidemic data from Chinese Center for Disease Control and Prevention, we first estimate the values of parameters in the model. Then the basic reproduction number of TB infection in the mainland China is calculated to be 1.0558. Since the

In this paper, we introduce a model to study the effects of human populations on fish survival in aquatic media. Directly, this occurs by fishing. Indirectly instead this is related to other human actions that lead to organic pollution and consequently low dissolved oxygen(DO) levels, thereby harming the aquatic fauna. Mathematically, we consider various nonlinear processes involving human population

In this paper, we use the classical Ross–Macdonald model to analyze the effect of the Mosquito Home System (MHS), which is an example of an auto-dissemination trap, in controlling the spread of dengue in Malaysia in a high-rise condominium environment. By using the national dengue data from Malaysia, we are able to estimate ł which represents the initial growth rate of the dengue epidemic and thus

Water level in rivers, lakes and reservoirs has great influence on the interactions between prey and predator fish. Indeed, the increase of the water volume hinders the capture of the prey by the predator. The same reasoning applies when there is a decrease in the volume of water, favoring the capture of the prey by the predator. In this paper, we consider a seasonally varying predator–prey model to

This paper proposes a mathematical model describing the dynamics of both Antarctic krill and Blue whale population where Antarctic krill species (prey) has group defense when they aggregate in herds in order to provide a self-defense from Blue whale species (predator). Firstly, a sufficient condition for the global asymptotical stability of the positive equilibrium is given using Poincaré–Bendixson

Microbial Fuel Cells (MFCs) are devices that generate electricity directly from organic compounds with microbes (electricigens) serving as anodic catalysts. As a novel environment-friendly energy source, MFCs have extensive practical value. Since the biological features and metabolic mechanism of electricigens have a great effect on the electricity production of MFCs, it is a big deal to screen strains

Influenza virus mutates frequently. This poses immense challenges to prevent the spread of influenza. This paper aims to investigate an influenza epidemic model in which influenza virus can mutate into a mutant influenza virus. We find a threshold condition that determines the stability of the disease-free equilibrium. Two equilibria may also exist: mutant-dominant equilibrium and endemic equilibrium

In this paper, an HIV infection model with eclipse phase, humoral immune response and immunological delay has been discussed. By studying the characteristic equations of the model, the local stability analysis of various equilibrium points has been explored. Treating the delay as the bifurcation parameter, it has been shown that the delay can destabilize the stability of the infected steady-state leading