Journal of Biological Dynamics最新文献

We present a systematic comparison and analysis of four discrete-time, host-parasitoid models. For each model, we specify that density-dependent effects occur prior to parasitism in the life cycle of the host. We compare density-dependent growth functions arising from the Beverton-Holt and Ricker maps, as well as parasitism functions assuming either a Poisson or negative binomial distribution for parasitoid attacks. We show that overcompensatory density-dependence leads to period-doubling bifurcations, which may be supercritical or subcritical. Stronger parasitism from the Poisson distribution leads to loss of stability of the coexistence equilibrium through a Neimark-Sacker bifurcation, resulting in population cycles. Our analytic results also revealed dynamics for one of our models that were previously undetected by authors who conducted a numerical investigation. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete-time model in order to promote communication and broader understanding.

We model the extent to which age-targeted protective sequestration can be used to reduce ICU admissions caused by novel coronavirus COVID-19. Using demographic data from New Zealand, we demonstrate that lowering the age threshold to 50 years of age reduces ICU admissions drastically and show that for sufficiently strict isolation protocols, sequestering one-third of the countries population for a total of 8 months is sufficient to avoid overwhelming ICU capacity throughout the entire course of the epidemic. Similar results are expected to hold for other countries, though some minor adaption will be required based on local age demographics and hospital facilities.

In this paper, we first investigate a stochastic two-predators one-prey model with Lévy noise and distributed delays. The global dynamical behaviour is discussed. The criteria on the existence of global positive solutions, stochastic boundedness, extinction and global asymptotic stability in the mean with probability one are established. And then, the harvesting for each species is introduced to the model. The optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY, for short) are further established.

In this paper, we formulate a stage-structured predator-prey model with mutual interference, in which includes two discrete delays. By theoretical analysis, we establish the stability of the unique positive equilibrium and the existence of Hopf bifurcation when the maturation delay for predators is used as the bifurcation parameter. Our results exhibit that the maturation delay for preys does not affect the stability of the positive equilibrium. However, the maturation delay for predator is able to destabilize the positive equilibrium and causes periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and display the differential impacts of two type delays and mutual interference.

In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [E. D'Aniello and S. Elaydi, The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems, Discr. Contin. Dyn. Series B. 2019 (to appear).], we embed the non-autonomous difference equations in an autonomous discrete dynamical systems in a higher dimension space, which is the product space of the phase space and the space of the functions defining the non-autonomous system. Our current approach applies to two scenarios. In the first scenario, we assume that the trait equations are decoupled from the equations of the populations. This requires specialized biological and ecological assumptions which we clearly state. In the second scenario, we do not assume decoupling, but rather we assume that the dynamics of the trait is known, such as approaching a positive stable equilibrium point which may apply to a much broader evolutionary dynamics.

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].

A deterministic model of onchocerciasis disease dynamics is considered in a community partitioned into compartments based on the disease status. Public health education is offered in the community during the implementation of mass treatment using ivermectin drugs. Also, larviciding and trapping strategies are implemented in the vector population with the aim of controlling population growth of black flies. We fit the model to the data to check the suitability of the model. Expressions are derived for the influence on the reproduction numbers of these strategies. Numerical results show that the dynamics of onchocerciasis and the growth of black flies are best controlled when the four strategies are implemented simultaneously. Also, the results suggest that for the elimination of the disease in the society there is a need for finding another drug which will be implemented to ineligible human as well as killing the adult worms instead of ivermectin.

Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizosphere. The sufficient conditions for existence of the order-1 periodic solution are obtained by using the geometrical theory of the impulsive semi-dynamical system. We show the impulsive control system tends to an order-1 periodic solution if the control measures are achieved. Furthermore, we investigate the stability of the order-1 periodic solution by means of a novel method introduced in the literature [Y. Ye, The Theory of the Limit Cycle, Shanghai Science and Technology Press, 1984.]. Finally, mathematical results are justified by some numerical simulations.

The outbreak of COVID-19 was first experienced in Wuhan City, China, during December 2019 before it rapidly spread over globally. This paper has proposed a mathematical model for studying its transmission dynamics in the presence of face mask wearing and hospitalization services of human population in Tanzania. Disease-free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. The trace-determinant approach was used in the local stability of disease-free equilibrium point while Lyapunov function technique was used to determine the global stability of both disease-free and endemic equilibrium points. Basic reproduction number, $R_0$ , was determined in which its numerical results revealed that, in the presence of face masks wearing and medication services or hospitalization as preventive measure for its transmission, $R_0=0.698$ while in their absence $R_0=3.8$ . This supports its analytical solution that the disease-free equilibrium point $E_0$ is asymptotically stable whenever $R_0<1$ , while endemic equilibrium point $E_{\ast }$ is globally asymptotically stable for $R_0>1$ . Therefore, this paper proves the necessity of face masks wearing and hospitalization services to COVID-19 patients to contain the disease spread to the population.