Journal of Biological Systems

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results.

In the proposed study, a nonlinear model is developed to explore the interactive dynamics between cattle and invertebrates when they coexist in a grassland system and compete with one another for the same resource — the grass biomass. The constructed model is theoretically investigated using the qualitative theory of differential equations to show the system’s rich dynamical properties, which are crucial for maintaining the ecosystem’s balance in grasslands. The qualitative findings show that, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. The model results support the idea that inter-specific competition between cattle and invertebrates does not always produce regular dynamic patterns but may also produce periodic and destabilizing patterns. The model’s outputs may assist in striking a balance between pasture and natural grass biomass in grassland with the invertebrates.

This paper deals with the dynamics of tuberculosis transmission model with different genders and age structures. The basic reproduction numbers ${{ℛ}}_0={{ℛ}}_F+{{ℛ}}_M$ are defined, where ${{ℛ}}_F$ and ${{ℛ}}_M$ are the basic reproduction number of tuberculosis transmission in female and male populations, respectively. The global stability of the disease-free equilibrium was discussed when ${{ℛ}}_0<1$; The existence, uniqueness and global stability of the endemic equilibrium, and the persistence of the system both were proved when ${{ℛ}}_0>1$. The findings indicate that the tuberculosis dynamical model with different genders and age structures will experience the classical threshold dynamic behaviors, that is, if ${{ℛ}}_0<1$, the disease will disappear; while if ${{ℛ}}_0>1$, the disease will spread within the population, and eventually lead to a endemic disease. Finally, the theoretical analysis of the model is verified by numerical simulation and we proposed that male infected individuals should be focused on in the prevention and control of tuberculosis in the future.

In this paper, the dynamics of a Filippov system with logistically growing prey and Holling Type II predation is explored. The selective nonlinear harvesting of prey is carried out when the ratio of prey to predator is above a specified threshold value. In order to prevent the extinction of both the species and sustainable economic gains, no harvesting is allowed when the ratio is below a threshold value. The equilibrium states and their stability for the individual smooth are analyzed. Filippov convex method is applied to determine the dynamics on the boundary. The sliding mode dynamics is scrutinized, and it is observed that there is no escaping region. The existence of boundary points, tangent points and pseudo-equilibrium points are established. The conditions are obtained for the visibility of the tangent points. The complex behavior within the sliding region is studied by experimenting with different initial conditions. The increase in harvesting effort may lead to extinction of both the species through the sliding region of the boundary. The change in the stability behavior of both the interior equilibrium states is investigated with respect to model parameters. Border cross bifurcates with threshold value as the bifurcation parameter is shown for both the interior equilibrium states.

In this paper, we develop an epidemic model with a nonlinear function that describes the saturated digital contact tracing. The model is theoretically and numerically analyzed based on its dynamics. The model equilibria points and the basic reproduction number are obtained. However, the proposed model reveals both backward and forward bifurcation, and backward bifurcation occurs when the digital contact tracing saturation parameter is larger than a specific threshold. Real data are used to fit the model and estimate the parameter values. Sensitivity analysis reveals that interventions such as reducing the infection rate, enhancing quarantine efforts, and accelerating vaccination can effectively reduce the basic reproduction number, $R_0$. Simulations show that improving tracing accuracy and encouraging greater participation in providing personal track information can effectively reduce the peak of undetected exposed individuals. Moreover, we analyze the expression for the specific threshold and determine that the increasing hospital resources and strengthening patient quarantine can reduce the potential occurrence of backward bifurcation. The analysis and simulations presented in this paper provide valuable suggestions for the prevention and control of the epidemic.

This paper considers predator–prey systems in which the predator adapts the search speed to prey’s density. The prey admits the cost of fear because of the predator and moves between source–sink patches to escape from predation. Using dynamical systems theory, we demonstrate equilibrium stability, uniform persistence and bifurcations in the system. It is shown that enhancing the search speed of predator and/or decreasing prey’s dispersal from the source to sink could promote persistence of the system, while increasing the fear cost would stabilize the system. Moreover, dispersal could make the prey persist in both source–sink patches, even drive the predator into extinction. The dispersal could also make the prey reach a total population abundance larger than that without dispersal, even larger than the carrying capacity. Asymmetry in dispersal plays a role in the persistence and abundance. A novel finding of this work is that dispersal may lead to results reversing those without dispersal. Numerical simulations illustrate and extend our results. This work is important in understanding complexity in predation systems.

This paper investigates the dynamical behavior of the modified May–Holling–Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. Detailed mathematical analysis and numerical evaluations, including the situation of ecosystem collapsing, have been presented to discuss the coexistence of species’, stability, occurrence of different bifurcations (saddle-node, transcritical, and Hopf) in three cases in the presence of prey and alternative resources, in the absence of prey and in the absence of alternative resources. It has been obtained that the multiple coexisting states and their stability are outcomes of variations in predation rate for alternative resources. Also, the occurrence of Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation are due to variations in the parameters of dynamic alternative resources. The impact of dynamic alternative resources on species’ density reveals the fact that if the predation rate for alternative resources increases, then the prey biomass increases (under some restrictions), and variations in the predator’s biomass widely depend upon the quality of food items. This study also points out that the survival of predators is possible in the absence of prey. In the theme of ecological balance, this study suggests some theoretical points of view for the eco-managers.

In reality, the dissemination of information about COVID-19 vaccines typically involves a combination of opinion leaders and self-organizing networks, with each node being exposed to information in varying ways. However, conventional models often assume homogeneity in networks, treating all nodes as equal in terms of propagation probabilities within a fixed timeframe, thereby neglecting the inherent heterogeneity of social networks in information dissemination. To address this limitation, we propose a novel semi-directed network model, referred to as the susceptible-forwarding-immune model, which incorporates the complex structure of actual social networks and classifies nodes based on their mode of contact and the number of users they reach within a specific period. We calibrated and validated our model using real data on COVID-19 vaccine information from the Chinese Sina microblog, and our sensitivity analysis yielded insights into optimal strategies for disseminating such information.

In this work, we studied the time-frequency dynamics of spike-wave discharges in rats with predisposition to absence epilepsy (WAG/Rij line) in two frequency ranges: 7–12,Hz and 14–24,Hz. The first and the second harmonics of the seizure main frequency lie in these ranges. Recordings of brain local field potentials of eight animals in eleven experiments of eight hour duration were analyzed. The method was based on the fast Fourier transform with a Hann’s window, and skeletons were constructed based on the obtained spectrograms. Using the skeletons, a visual and automated numerical assessment of the main frequency evolution was performed. As a result of this analysis, it was shown that temporal dynamics of the main frequency in the range 14–24,Hz follows the dynamics of the main frequency in the range 7–12,Hz. Since during the baseline activity the main frequencies in two considered ranges were developing independently, our finding indicates that the discharge is a significantly nonlinear process.

In this paper, we investigate the impact of catheterization on swallowing if esophagus suffers from a hiatus hernia. It is modeled as a partially diverging tube having a peripheral layer of different viscosity besides the core layer. The model duly considers mass conservation in the two layers separately. It is inferred that even in the presence of a catheter inside esophagus, any sliding herniation requires less pressure for flow, i.e., swallowing will be easier if the esophagus diverges more near the cardiac sphincter. However, the presence of a catheter requires esophagus to work more in order to swallow the same quantity. Pressure enhances by many folds, but its distribution remains similar. The time-averaged flow rate and the maximum pressure, restraining fluid from swallowing, give some clues about a catheterized herniated esophagus. The flow enhances for a thinner peripheral layer. A more viscous peripheral layer as well favors flow. However, the thickness of the catheter hinders swallowing. This is to be taken care of while a patient undergoes any catheterized treatment. Increasing wave amplitude and dilating parameters can enhance flow in the presence of a catheter. It is also concluded that the frictional forces exerted by the tube wall on the peripheral layer increase in the catheter’s presence.

In this paper, a deterministic size-dependent phytoplankton–zooplankton (PZ) model with additive Allee effect as well as its stochastic differential equation version is formulated to explore the growth dynamic of phytoplankton. A stability and Hopf bifurcation analysis is performed towards deterministic PZ model, and stochastic dynamic analysis is carried out on the stochastic PZ model, including the stochastic extinction, persistence in mean and the unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulation analysis. Numerical simulations reveal that the synergistic effect of plankton body size and Allee effect can have a complex impact on the growth of phytoplankton in the deterministic and stochastic environments. One of the most interesting findings suggests that the reduced phytoplankton cell size can trigger bistable phenomenon, while the increased phytoplankton cell size or the weakened Allee effect has the ability to destroy such bistable phenomenon.

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.