Journal of Biological Dynamics最新文献

We introduce a compartmental host-vector model for dengue with two viral strains, temporary cross-immunity for the hosts, and possible secondary infections. We study the conditions on existence of endemic equilibria where one strain displaces the other or the two virus strains co-exist. Since the host and vector epidemiology follow different time scales, the model is described as a slow-fast system. We use the geometric singular perturbation technique to reduce the model dimension. We compare the behaviour of the full model with that of the model with a quasi-steady approximation for the vector dynamics. We also perform numerical bifurcation analysis with parameter values from the literature and compare the bifurcation structure to that of previous two-strain host-only models.

This note provides an elementary derivation of the basic reproduction number and the effective reproduction number from the discrete Kermack-McKendrick epidemic model. The derived formulae match those derived from the continuous version of the model; however, the derivation from discrete model is a bit more intuitive. The MATLAB functions for its calculation are given. A real case example is considered and the results are compared with those obtained by the R0 and the EpiEstim software packages.

It is widely recognized that the criminal act of poaching has brought tremendous damage to biodiversity. This paper employs a stochastic single-species model with regime switching to investigate the impact of poaching. We first carry out the survival analysis and obtain sufficient conditions for the extinction and persistence in mean of the single-species population. Then, we show that the model is positive recurrent by constructing suitable Lyapunov function. Finally, numerical simulations are carried out to support our theoretical results. It is found that: (i) As the intensity of poaching increases, the odds of being at risk of extinction increases for the single-species population. (ii) The regime switching can suppress the extinction of the single-species population. (iii) The white noise is detrimental to the survival of the single-species population. (iv) Increasing the criminal cost of poaching and establishing animal sanctuaries are important ways to protect biodiversity.

Basic reproduction number $R_0$ in network epidemic dynamics is studied in the case of stochastic regime-switching networks. For generality, the dependence between successive networks is considered to follow a continuous time semi-Markov chain. $R_0$ is the weighted average of the basic reproduction numbers of deterministic subnetworks. Its position with respect to 1 can determine epidemic persistence or extinction in theories and simulations.

Co-feeding is a mode of pathogen transmission for a wide range of tick-borne diseases where susceptible ticks can acquire infection from co-feeding with infected ticks on the same hosts. The significance of this transmission pathway is determined by the co-occurrence of ticks at different stages in the same season. Taking this into account, we formulate a system of differential equations with tick population dynamics and pathogen transmission dynamics highly regulated by the seasonal temperature variations. We examine the global dynamics of the model systems, and show that the two important ecological and epidemiological basic reproduction numbers can be used to fully characterize the long-term dynamics, and we link these two important threshold values to efficacy of co-feeding transmission.

The dynamic mechanism of a whole-cell model containing electrical signalling and two-compartment Ca${}^{2+}$ signalling in gonadotrophs is investigated. The transition from spiking to bursting by Hopf bifurcation of the fast subsystem about the slow variable is detected via the suitable parameters. When the timescale of K${}^{+}$ gating variable is changed, the relaxation oscillation with locally small fluctuation, chaotic bursting and mixed-mode bursting (MMB) are revealed through chaos. In addition, the bifurcation of $[{Ca}^{2+}{]}_i$ with regard to $\left[I{P}_3\right]$ is analysed, showing periodic solutions, torus, period doubling solutions and chaos. Finally, hyperpolarizations and torus canard-like behaviours of the full system under a set of specific parameters are elucidated.

In a recent paper, Che et al. [5] used a continuous-time Ordinary Differential Equation (ODE) model with risk structure to study cholera infections in Cameroon. However, the population and the reported cholera cases in Cameroon are censored at discrete-time annual intervals. In this paper, unlike in [5], we introduce a discrete-time risk-structured cholera model with no spatial structure. We use our discrete-time demographic equation to 'fit' the annual population of Cameroon. Furthermore, we use our fitted discrete-time model to capture the annually reported cholera cases from 1987 to 2004 and to study the impact of vaccination, treatment and improved sanitation on the number of cholera infections from 2004 to 2019. Our discrete-time cholera model confirms the results of the ODE model in [5]. However, our discrete-time model predicts a decrease in the number of cholera cases in a shorter period of cholera intervention (2004-2019) as compared to the ODE model's period of intervention (2004-2022).

To investigate the release strategies of sterile mosquitoes for the wild population control, we propose mathematical models for the interaction between two-mosquito populations incorporating impulsive releases of sterile ones. The long-term control model is first studied, and the existence and stability of the wild mosquito-extinction periodic solution are exploited. Thresholds of the release amount and release period which can guarantee the elimination of the wild mosquitos are obtained. Then for the limited-time control model, three different optimal strategies in impulsive control are investigated. By applying a time rescaling technique and an optimization algorithm based on gradient, the optimal impulsive release timings and amounts of sterile mosquitoes are obtained. Our results show that the optimal selection of release timing is more important than the optimal selection of release amount, while mixed optimal control has the best comprehensive effect.

We study a population model where cells in one part of the cell cycle may affect the progress of cells in another part. If the influence, or feedback, from one part to another is negative, simulations of the model almost always result in multiple temporal clusters formed by groups of cells. We study regions in parameter space where periodic 'k-cyclic' solutions are stable. The regions of stability coincide with sub-triangles on which certain events occur in a fixed order. For boundary sub-triangles with order '$rs1$', we prove that the k-cyclic periodic solution is asymptotically stable if the index of the sub-triangle is relatively prime with respect to the number of clusters k and neutrally stable otherwise. For negative linear feedback, we prove that the interior of the parameter set is covered by stable sub-triangles, i.e. a stable k-cyclic solution always exists for some k. We observe numerically that the result also holds for many forms of nonlinear feedback, but may break down in extreme cases.

A discrete-time deterministic epidemic model is proposed to better understand the contagious dynamics and the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model both in a random-mixing approach and in a small-world network formulation. The models include the basic parameters that characterize an epidemic: infection and recovery times, as well as mechanisms of contagion. Depending on the parameters, the random-mixing model has different types of behaviour of an epidemic: pathogen extinction; endemic infection; sustained oscillations and dynamic extinction. Spatial effects are included in our network-based approach, where each individual of a population is represented by a node of a small-world network. Our network-based approach includes rewiring connections to account for time-varying network structure, a consequence of the natural response to the emergence of an epidemic (e.g. avoiding contacts with infected individuals). Random and adaptive rewiring conditions are analysed and numerical simulation are made. A comparison of model predictions with the actual effects of COVID-19 infection on population that occurred in Italy and France is produced. Results of the time series of infected people show that our adaptive evolving networks represent effective strategies able to decrease the epidemic spreading.