Journal of Biological Systems最新文献

Dynamical systems described by deterministic differential equations represent idealized situations where random implications are ignored. In the context of biomathematical modeling, the introduction of random noise must be distinguished between environmental (or extrinsic) noise and demographic (or intrinsic) noise. In this last context it is assumed that the variation over time is due to demographic variation of two or more interacting populations, and not to fluctuations in the environment. The modeling and simulation of demographic noise as a stochastic process affecting single units of the populations involved in the model are well known in the literature and they result in discrete stochastic systems. When the population sizes are large, these discrete stochastic processes converge to continuous stochastic processes, giving rise to stochastic differential equations. If noise is ignored, these stochastic differential equations turn to ordinary differential equations. The inverse process, i.e., inferring the effects of demographic noise on a natural system described by a set of ordinary differential equations, is an issue addressed in a recent paper by Carletti M, Banerjee M, A backward technique for demographic noise in biological ordinary differential equation models, Mathematics7:1204, 2019. In this paper we show an example of how the technique to model and simulate demographic noise going backward from a deterministic continuous differential system to its underlying discrete stochastic process can provide a discrepancy effect, modifying the dynamics of the deterministic model.

In this paper, a predator–prey system with multiple anti-predator behaviors is developed and studied, where not only the prey may spread between patches but also the fear effect and counter-attack behavior of the prey are taken into account. First, the stability and existence of coexistence equilibria are presented. The unique positive equilibrium may be a saddle-node or a cusp of codimension 2. Then, various transversality conditions of bifurcations such as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are obtained. Moreover, compared with a single strategy, the multiple anti-predator strategies are more beneficial to the persistence and the population density of prey.

The summary measurement of an epidemic such as the final size is an important quantity that allows us to approximate the impact of the disease on the affected region. In recent years, final size measurements for vector-transmitted diseases have acquired importance because of the increased concern for mosquito-borne diseases like dengue, Zika, Chikungunya, etc. However, analytical expressions for this estimate in the stage-structured models applicable to vector-borne diseases are less, mostly focused on the classical Kermack–McKendrick model. In this paper, we first calculate the final size expressions for an SIR model with carrier state and a SEIR–SI host–vector model. Then we extend this for the SEIR–SI host–vector model with treatment class in the host, as well as for the model with vertical transmission in the vector population. Finally, we verify our final size expression with some real scenarios.

Chronic Myeloid Leukemia (CML) is a biphasic malignant clonal disorder that progresses, first with a chronic phase, where the cells have enhanced proliferation only, and then to a blast phase, where the cells have the ability of self-renewal. It is well recognized that the Philadelphia chromosome (which contains the BCR-ABL fusion gene) is the “hallmark of CML”. However, empirical studies have shown that the mere presence of BCR-ABL may not be a sufficient condition for the development of CML, and further modifications related to tumor suppressors may be necessary. Accordingly, we develop a three-mutation stochastic model of CML progression, with the three stages corresponding to the non-malignant cells with BCR-ABL presence, the malignant cells in the chronic phase, and the malignant cells in the blast phase. We demonstrate that the model predictions agree with age incidence data from the United States. Finally, we develop a framework for the retrospective estimation of the time of onset of malignancy, from the time of detection of the cancer.