Journal of Mathematical Biology最新文献

A dynamic reaction-diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment.

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number ({mathcal {R}}_0) and show that the disease-free periodic solution is globally attractive when ({mathcal {R}}_0<1) whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when ({mathcal {R}}_0>1). Moreover, we find that ({mathcal {R}}_0) is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle’s invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays.

In this paper, we propose a reaction–advection–diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number ( Re _{0} ) for this model and show that ( {Re _0} ) is a threshold parameter: if ( {Re _0} <1 ), then the disease-free periodic solution is globally attractive; if ( {Re _0}>1 ), the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on ( Re _{0}). Our findings indicate that ignoring seasonality may underestimate (Re _0). Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission.

Insect growth regulators (IGRs) have been developed as effective control measures against harmful insect pests to disrupt their normal development. This study is to propose a mathematical model to evaluate the cost-effectiveness of IGRs for pest management. The key features of the model include the temperature-dependent growth of insects and realistic impulsive IGRs releasing strategies. The impulsive releases are carefully modeled by counting the number of implements during an insect’s temperature-dependent development duration, which introduces a surviving probability determined by a product of terms corresponding to each release. Dynamical behavior of the model is illustrated through dynamical system analysis and a threshold-type result is established in terms of the net reproduction number. Further numerical simulations are performed to quantitatively evaluate the effectiveness of IGRs to control populations of harmful insect pests. It is interesting to observe that the time-changing environment plays an important role in determining an optimal pest control scheme with appropriate release frequencies and time instants.

In this work, we formulate a random Wolbachia invasion model incorporating the effects of imperfect maternal transmission and incomplete cytoplasmic incompatibility (CI). Under constant environments, we obtain the following results: Firstly, the complete invasion equilibrium of Wolbachia does not exist, and thus the population replacement is not achievable in the case of imperfect maternal transmission; Secondly, imperfect maternal transmission or incomplete CI may obliterate bistability and backward bifurcation, which leads to the failure of Wolbachia invasion, no matter how many infected mosquitoes would be released; Thirdly, the threshold number of the infected mosquitoes to be released would increase with the decrease of the maternal transmission rate or the intensity of CI effect. In random environments, we investigate in detail the Wolbachia invasion dynamics of the random mosquito population model and establish the initial release threshold of infected mosquitoes for successful invasion of Wolbachia into the wild mosquito population. In particular, the existence and stability of invariant probability measures for the establishment and extinction of Wolbachia are determined.

The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at all scales, including at the scale of a few individuals. Local spatial aggregation can hinder competitive exclusion since individuals then interact mostly with other individuals of their own species, rather than competitors from different species. To evaluate how microscale spatial aggregation might explain phytoplankton diversity maintenance, an individual-based, multispecies representation of cells in a hydrodynamic environment is required. We formulate a three-dimensional and multispecies individual-based model of phytoplankton population dynamics at the Kolmogorov scale. The model is studied through both simulations and the derivation of spatial moment equations, in connection with point process theory. The spatial moment equations show a good match between theory and simulations. We parameterized the model based on phytoplankters’ ecological and physical characteristics, for both large and small phytoplankton. Defining a zone of potential interactions as the overlap between nutrient depletion volumes, we show that local species composition—within the range of possible interactions—depends on the size class of phytoplankton. In small phytoplankton, individuals remain in mostly monospecific clusters. Spatial structure therefore favours intra- over inter-specific interactions for small phytoplankton, contributing to coexistence. Large phytoplankton cell neighbourhoods appear more mixed. Although some small-scale self-organizing spatial structure remains and could influence coexistence mechanisms, other factors may need to be explored to explain diversity maintenance in large phytoplankton.

Human mobility, which refers to the movement of people from one location to another, is believed to be one of the key factors shaping the dynamics of the COVID-19 pandemic. There are multiple reasons that can change human mobility patterns, such as fear of an infection, control measures restricting movement, economic opportunities, political instability, etc. Human mobility rates are complex to estimate as they can occur on various time scales, depending on the context and factors driving the movement. For example, short-term movements are influenced by the daily work schedule, whereas long-term trends can be due to seasonal employment opportunities. The goal of the study is to perform literature review to: (i) identify relevant data sources that can be used to estimate human mobility rates at different time scales, (ii) understand the utilization of variety of data to measure human movement trends under different contexts of mobility changes, and (iii) unraveling the associations between human mobility rates and social determinants of health affecting COVID-19 disease dynamics. The systematic review of literature was carried out to collect relevant articles on human mobility. Our study highlights the use of three major sources of mobility data: public transit, mobile phones, and social surveys. The results also provides analysis of the data to estimate mobility metrics from the diverse data sources. All major factors which directly and indirectly influenced human mobility during the COVID-19 spread are explored. Our study recommends that (a) a significant balance between primitive and new estimated mobility parameters need to be maintained, (b) the accuracy and applicability of mobility data sources should be improved, (c) encouraging broader interdisciplinary collaboration in movement-based research is crucial for advancing the study of COVID-19 dynamics among scholars from various disciplines.

We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the incidence of light on a tree (and hence how fast it grows) is affected by shading by taller trees. The classic formulation of a model for such a size-structured population employs a first order quasi-linear partial differential equation equipped with a non-local boundary condition. However, the model can also be formulated as a delay equation, more specifically a scalar renewal equation, for the population birth rate. After discussing the well-posedness of the delay formulation, we analyse how many stationary birth rates the equation can have in terms of the functional parameters of the model. In particular we show that, under reasonable and rather general assumptions, only one stationary birth rate can exist besides the trivial one (associated to the state in which there are no individuals and the population birth rate is zero). We give conditions for this non-trivial stationary birth rate to exist and analyse its stability using the principle of linearised stability for delay equations. Finally, we relate the results to the alternative, partial differential equation formulation of the model.

In this paper, we study in detail the structure of the global attractor for the Lotka–Volterra system with a Volterra–Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.