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.

Reverse transcriptase (RT) and integrase (IN) are two pivotal enzymes in HIV-1 replication. RT converts the single-stranded viral RNA genome into double-stranded DNA and IN catalyzes the integration of viral double-stranded DNA into host DNA. Currently, dual inhibitors of HIV-1 RT and IN have become a hotspot in new anti-HIV drug research and development. A dual inhibitor of HIV-1 RT/IN does the same thing as the two independent drugs would do. In this paper, we develop a mathematical model comprising a system of nonlinear differential equations describing HIV-1 RT/IN catalyzed biochemical reactions based on Michaelis–Menten enzyme kinetic reaction. In the formulated model we incorporate HIV-1 RT/IN dual inhibitor which simultaneously works as a non-nucleoside RT inhibitor and IN inhibitor. To examine the efficacy of HIV-1 RT/IN dual inhibitor in the treatment of HIV-1 infection, we have introduced a one-dimensional impulsive differential equation model and determined an effective dosing regimen for applying the inhibitor numerically. Furthermore, the exact closed form solution of the impulsive differential equation model is carried out by using the Lambert W function and the local stability of the periodic solution is also obtained analytically. The results obtained from analytical as well as numerical studies provide a basic idea to investigate the minimum dose with the highest efficacy for administering HIV-1 RT/IN dual inhibitors to prevent HIV-1 infection.

In this paper, we designed a population model that shows how a prey species defends itself against a generalist predator by exhibiting group defence. A non-monotonic functional response is used to represent the group defence functionality. We have demonstrated the model’s local stability in the vicinity of the coexisting equilibrium solution employing a local Lyapunov function. Condition for existence of Hopf bifurcation is obtained along with its normal form. The suggested model has been validated by numerical simulations, which have also been used to verify the acquired analytical results. The parameters are subjected to sensitivity analysis by utilizing partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS). The Z-type dynamic method is used to prevent population blow-up.

The sterile insect technique (SIT) is a biological control technique that can be used either to eliminate or decay a wild mosquito population under a given threshold to reduce the nuisance or the epidemiological risk. In this work, we propose a model using a differential system that takes into account the variations of rainfall and temperature over time and study their impacts on sterile males’ releases strategies. Our model is as simple as possible to avoid complexity while being able to capture the temporal variations of an Aedes albopictus mosquito population in a domain treated by SIT, located in Réunion island. The main objective is to determine what period of the year is the most suitable to start a SIT control to minimize the duration of massive releases and the number of sterile males to release, either to reduce the mosquito nuisance, or to reduce the epidemiological risk. Since sterilization is not $100\%$ efficient, we also study the impact of different levels of residual fertility within the released sterile males population. Our study shows that rainfall plays a major role in the dynamics of the mosquito and the SIT control, that the best period to start a massive SIT treatment lasts from July to December, that residual fertility has to be as small as possible, at least for nuisance reduction. Indeed, when the main objective is to reduce the epidemiological risk, we show that residual fertility is not necessarily an issue. Increasing the size of the releases is not always interesting. We also highlight the importance of combining SIT with mechanical control, i.e., the removal of breeding sites, in particular when the initial mosquito population is large. Last but not least our study shows the usefulness of the modeling approach to derive various simulations to anticipate issues and demand in terms of sterile insects’ production.