Journal of Mathematical Biology最新文献

Antiviral therapies can yield different outcomes depending on their scheduling: a highly effective drug may produce treatment results ranging from successful to inconsequential, depending on therapeutic timing, dosing intervals, and dosage. The effectiveness of antiviral therapies can be assessed using mathematical models that describe viral spread within a host. In this work, we conduct a study based on the dynamic characterization of a target-cell model to address a multi-objective control problem aimed at designing highly effective and host-customizable antiviral therapies. These therapies involve finite-time antiviral treatments that minimize the viral load peak and the infection final size until infection clearance, while simultaneously reducing the total amount of drug intake as much as possible. Two optimization-based control strategies are proposed: a fixed-dose and a variable-dose approach. The variable-dose strategy achieves superior performance by explicitly considering the system dynamics in the design of the control. Simulation results, based on an identified model for COVID-19 patients treated with Paxlovid, illustrate the potential benefits of the proposed strategies.

This paper is concerned with asymptotic behavior of the basic reproduction number defined by next generation nonlocal (convolution) dispersal operators in a time-periodic environment and applications. First we investigate the influence of the frequency and dispersal rate on the basic reproduction number, and we obtain that the basic reproduction number is monotone on the frequency. In the nonautonomous situation, the basic reproduction number is not a monotone function of dispersal rate in general. We derive the monotonicity for large frequency or dispersal rate. Then we apply the obtained results to a time-periodic SIS epidemic model and establish the existence and asymptotic profiles of the endemic periodic solution. Since solution maps of nonlocal system lack compactness, the standard uniform persistence theory and topological degree theory are unapplicable to obtain the existence of the endemic periodic solution. To overcome this difficulty, we apply the asymptotic fixed point theorem with the help of the Kuratowski measure of noncompactness.

This paper aims to investigate the benthic-drift population model in both open and closed advective environments, focusing on the logistic growth of benthic populations. We obtain the threshold dynamics using the monotone iteration method, and show that the zero solution is globally attractive straightforward when linearly stable. When unstable, limits from monotonic iteration of upper and lower solutions are upper and lower semi-continuous, respectively. By employing a part metric, we prove these limits are equal and continuous, leading to a positive steady state. In the critical case, we establish that the limit function from the upper solution iteration must be the zero solution by analyzing an algebraic equation. Furthermore, we conduct a quantitative analysis of the principal eigenvalue for a non-self-adjoint eigenvalue problem to examine how the diffusion rate, advection rate, and population release rates influence the dynamics. The results suggest that the diffusion rate and advection rate have distinct effects on population dynamics in open and closed advective environments, depending on the population release rates.

Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an autocatalytic protein progression. The growth and transport of these assemblies depend on various mechanisms that can be targeted therapeutically. Here, we use spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain to study the effect of different drugs on whole-brain Alzheimer's disease progression.

We build and study an individual based model of the telomere length's evolution in a population across multiple generations. This model is a continuous time typed branching process, where the type of an individual includes its gamete mean telomere length and its age. We study its Malthusian's behaviour and provide numerical simulations to understand the influence of biologically relevant parameters.

In the past several decades, much attention has been focused on the effects of dispersal on total populations of species. In Zhang (EL 20:1118-1128, 2017), a rigorous biological experiment was performed to confirm the mathematical conclusion: Dispersal tends to enhance populations under a suitable hypothesis. In addition, mathematical models keeping track of resource dynamics in population growth were also proposed in Zhang (EL 20:1118-1128, 2017) to understand this remarkable phenomenon. In these models, the self-regulated quantity "loss rate" of the population seems, in general, difficult to measure experimentally. Our main goal in this paper is to study the effects of relations between the loss rate and the resources, the role of dispersal, and the impact of their interactions on total populations. We compare the total population for small and large diffusion under various correlations between loss rate and the resources. Biological evidence seems to support some specific correlations between the loss rate and the resources.

We analyze the Lotka-Volterra n prey-1 predator system with no direct interspecific interaction between prey species, in which every prey species undergoes the effect of apparent competition via a single shared predator with all other prey species. We prove that the considered system necessarily has a globally asymptotically stable equilibrium, and we find the necessary and sufficient condition to determine which of feasible equilibria becomes asymptotically stable. Such an asymptotically stable equilibrium shows which prey species goes extinct or persists, and we investigate the composition of persistent prey species at the equilibrium apparent competition system. Making use of the results, we discuss the transition of apparent competition system with a persistent single shared predator through the extermination and invasion of prey species. Our results imply that the long-lasting apparent competition system with a persistent single shared predator would tend toward an implicit functional homogenization in coexisting prey species, or would transfer to a 1 prey-1 predator system in which the predator must be observed as a specialist (monophagy).

Wild birds are one of the main natural reservoirs for avian influenza viruses, and their migratory behavior significantly influences the transmission of avian influenza. To better describe the migratory behavior of wild birds, a system of reaction-advection-diffusion equations is developed to characterize the interactions among wild birds, poultry, and humans. By the next-generation operator, the basic reproduction number of the model is formulated. Then the threshold dynamic of the model is explored by some techniques including the theory of uniform persistence, internally chain transitive sets, and so on. Subsequently, the sensitivity analysis of parameters associated with the basic reproduction number is implemented. According to the temporal and spatial overlapping relationship between wild blue-winged ducks and poultry in North America, the effect of this relationship on the characteristic of spatial-temporal distribution of the viruses is well studied. Additionally, the risk of virus transmission from wild birds to poultry and humans is evaluated. The main results highlight that the basic reproduction number is more significantly affected by the parameters related to wild birds. Interestingly, the model output regarding the spatial distribution of poultry infections is consistent with the actual findings. Moreover, the risk of virus spillover from wild birds into poultry and humans varies with wild bird behavior and has a more substantial impact on poultry. Throughout this study, the critical risk points in the transmission process are identified, providing a theoretical basis for the prevention and control of avian influenza.

In this paper, a novel age-structured epidemiological model that simultaneously considers multiple viral strains is proposed. We develop a numerical framework for the study of the dynamics and optimal control by a linearly implicit Euler method, in which the biological meaning is unconditionally preserved. The first order convergence of numerical solutions in a finite time is derived from a uniform numerical boundedness. Moreover, the numerical dynamics are determined by a numerical basic reproduction number $R_h$ , which reflects the asymptotic stability of the equilibrium points. The abstract framework offers an effective and unified approach to study the long-time behaviour of multi-strain epidemic models that cover a wide variety of well-known models, which also provides a numerical optimal control strategy of the multi-strain age-structured SIR model. Finally, some numerical simulations illustrate the verification and the efficiency of our results.

Networked evolutionary game theory is a well-established framework for modeling the evolution of social behavior in structured populations. Most of the existing studies in this field have focused on 2-strategy games on heterogeneous networks or n-strategy games on regular networks. In this paper, we consider n-strategy games on arbitrary networks under the pairwise comparison updating rule. We show that under the limit of weak selection, the short-run behavior of the stochastic evolutionary process can be approximated by replicator equations with a transformed payoff matrix that involves both the average value and the variance of the degree distribution. In particular, strongly heterogeneous networks can facilitate the evolution of the payoff-dominant strategy. We then apply our results to analyze the evolutionarily stable strategies in an n-strategy minimum-effort game and two variants of the prisoner's dilemma game. We show that the cooperative equilibrium becomes evolutionarily stable when the average degree of the network is low and the variance of the degree distribution is high. Agent-based simulations on quasi-regular, exponential, and scale-free networks confirm that the dynamic behaviors of the stochastic evolutionary process can be well approximated by the trajectories of the replicator equations.