Journal of Biological Systems

Healthcare is indeed an inevitable part of life for everyone. In recent days, most of the deaths have been happening because of noncommunicable diseases. Despite the significant advancements in medical diagnosis, cardiovascular diseases are still the most prominent cause of mortality worldwide. With recent innovations in Machine Learning (ML) and Deep Learning (DL) techniques, there has been an enormous surge in the clinical field, especially in cardiology. Several ML and DL algorithms are useful for predicting cardiovascular diseases. The predictive capability of these algorithms is promising for various cardiovascular diseases like coronary artery disease, arrhythmia, heart failure, and others. We also review the lung interactions during heart disease. After the study of various ML and DL models with different datasets, the performance of the various strategies is analyzed. In this study, we focused on the analysis of various ML and DL algorithms to diagnose cardiovascular disease. In this paper, we also presented a detailed analysis of heart failure detection and various risk factors. This paper may be helpful to researchers in studying various algorithms and finding an optimal algorithm for their dataset.

In this paper, we developed an optimal control of a reaction–diffusion mathematical model, describing the spatial spread of dengue infection. Compartments for human and vector populations are considered in the model, including a compartment for the aquatic phase of mosquitoes. This enabled us to discuss the vertical transmission effects on the spread of the disease in a two-dimensional domain, using demographic data for different scenarios. The model was analyzed, establishing the existence and convergence of the weak solution for the model. The convergence of the numerical scheme to the weak solution was proved. For numerical approximation, we adopted the finite element scheme to solve direct and adjoint state systems. We also used the nonlinear gradient descent method to solve the optimal control problem, where the optimal management of government investment was proposed and leads to more effective dengue fever infection control. These results may help us understand the complex dynamics driven by dengue and assess the public health policies in the control of the disease.

An age-structured vector-borne disease model with horizontal transmission is proposed and studied in this paper, where the incubation ages of both host and vector and the immunity age of host are also introduced to consider the effects of multi-class-age structure. The reproductive number ${{ℛ}}_0$ is derived as a threshold value to determine the existence and stability of the disease-free and endemic steady states. Furthermore, by constructing suitable Lyapunov functionals, the global threshold dynamics of this model is established by ${{ℛ}}_0$, that is, the disease-free equilibrium is globally asymptotically stable when ${{ℛ}}_0<1$, while if ${{ℛ}}_0>1$ the endemic equilibrium is globally asymptotically stable. In addition, considering the limited budget of the centers for disease control and prevention (CDC) in the process of disease control, we present an optimal control problem with a fixed total expenditure, and discuss the existence of the most control strategy for this disease. Finally, some numerical simulations are performed to support the theoretical results.

In this paper, a predator–prey model with prey refuge was developed to investigate how prey refuge affect the dynamics of predator–prey interaction. We studied the existence and stability of equilibria, and then derived the sufficient conditions for the bifurcation such as saddle-node, transcritical, Hopf and Bogdanov–Takens bifurcation. In addition, a series of numerical simulations were carried out to illustrate the theoretical analysis, and the numerical results are consistent with the analytical results. Our results demonstrate that prey refuge has a great impact on the predator–prey dynamics.

A mathematical model considering two strains of hepatitis B virus (HBV) chronic carriers, to assess the impact of dose-structured imperfect vaccine, in a population, is designed and analyzed. The model is shown to have a locally and globally asymptotically stable disease-free equilibrium (DFE) whenever its associated reproduction number is numerically less than unity. Numerical analysis of the model shows that with the expected 50% minimum efficacy of the first vaccine dose, vaccinating 55% of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of hepatitis B infection. Such effective control can also be achieved if 50% of the first vaccine dose recipients take the second dose. Threshold analysis reveals that an imperfect HBV vaccine should have positive or negative population-level effect. Latin hypercube sampling–PRCC analysis illustrates that disease transmission rate, birth rate, natural death rate and proportion of children born with maternal immunity are most influential parameters in the disease dynamics. In this paper, the sensitivity analysis based on mathematical and in addition statistical techniques have been performed to determine the significance of the model parameters. It is observed that a number of the parameters play an important role to determine the magnitude of the basic reproduction number. Sensitivity analysis is achieved to determine model parameters’ importance in disease dynamics. It is observed that the reproduction number is the most responsive quantity to the potent transmission rate of HBV and in addition also vital to control the spread of the disease.

The Trojan Y Chromosome (TYC) strategy is a biological control method for controlling invasive populations with an XX–XY sex determinism, wherein a modified organism is introduced into an invasive population to skew the sex ratio over time, causing local extinction. However, the classical three compartment TYC model possesses blow-up solutions, for large initial conditions [Takyi EM, Beauregard MA, Griffin T, Bobo L, Parshad RD, On large and small data blow-up solutions in the Trojan Y Chromosome model, Axioms 11(3):120, 2022]. We investigate model improvements via accounting for a modified logistic term, female mating preference, competition between males and supermales and pair formation. Each one of these models is dynamically explored and is shown to possess global in-time non-negative solutions, in any parameter and initial data regime, and the models are also effective in facilitating extinction of the invasive wild type.

Immunotherapy has become a rapidly developing approach in the treatment of cancer. Cancer immunotherapy aims at promoting the immune system response to react against the tumor. In view of this, we develop a mathematical model for immune–tumor interplays with immunotherapeutic drug, and strategies for optimally administering treatment. The tumor–immune dynamics are given by a system of five coupled nonlinear ordinary differential equations which represent the interaction among tumor-specific CD4+T cells, tumor-specific CD8+T cells, tumor cells, dendritic cells and the immuno-stimulatory cytokine interleukin-2 (IL-2), extended through the addition of a control function describing the application of a dendritic cell vaccination. Dynamical behavior of the system is studied from the analytical as well as numerical points of view. The main aim is to investigate the treatment regimens which minimize the tumor cell burden and the toxicity of dendritic cell vaccination. Our numerical simulations demonstrate that the optimal treatment strategies using dendritic cell vaccination reduce the tumor cell burden and increase the cell count of CD4+T cells, CD8+T cells, dendritic cells and IL-2. The most influential parameters having significant impacts on the tumor cells are identified by employing the approach of global sensitivity analysis.

In this paper, we investigate the dynamics of a predator–prey system of an ecological community in which the fear instigated by the predators has an adverse effect on the reproduction rate of prey species, and also on the competition among themselves due to the limited environmental resources. To capture and handle the realistic scenario in a more meaningful way, we have mathematically built up the model system with the assumption that the predators predate on the prey items following Cosner functional response, which increases with increments in the prey and predator populations. The model system has been studied through noteworthy mathematical analysis and an extensive numerical simulation. Our simulation results demonstrate that the predator–prey system stabilizes due to predator’s induced fear suppressing/enhancing the birth/death of prey species. The competition among the predators for the available prey items also has a stabilizing role on the system’s dynamics. In contrast, the increasing growth rate of prey species or predation rate creates instability in the system by changing the stable phase to the limit cycle oscillations. Moreover, the effects of seasonality are also studied by extending the model system to its nonautonomous counterpart. Sufficient conditions are derived so that the seasonally driven system exhibits at least one positive periodic solution. Our numerical results show that the seasonally forced system exhibits periodic solution (globally attractive periodic solution), higher periodic solutions, bursting patterns and the extinction of predator species due to the seasonal variations of some parameters.

In this paper we present a model for a possible containment way of alien species invasions. It relies on the application of one or more stripes on the ground for which the survival conditions are harsher. After reviewing a number of possible threats for biodiversity that are the main motivation of this study, as well as a few instances of landscape disruption, we present a reaction–diffusion model and report the simulations results in various conditions. The inferences indicate that the diffusion process can be delayed, through the use of multiple obstacles, thereby allowing the possibility of taking alternative measures in order to contain the invasion, at least for some time. We discuss the diffusion delay in terms of the level of hostility, the length and the number of consecutive repetitions of the harsh environments. Comparisons on the parameter space show that the harshness and structural characteristics of the stripes are intertwined in a non-trivial way. Alternatively, the model can be used to ascertain the situations in which a population living in a territory can still thrive when its habitat is broken by artifacts, whether human-built or resulting from natural causes. Examples of this sort are presented in the final discussion.

In recent years, the stability of the predator–prey model subject to the Allee effect has become an interesting issue. This study investigates the effect of Allee effect on the stability of a discrete-time predator–prey model with Holling type-II functional response. Using equilibrium analysis, stability analysis and bifurcation theory, the mathematical characteristics of the proposed model are examined. Model experiences flip bifurcation and Neimark–Sacker bifurcation based on the center manifold theorem and bifurcation theory. Our analytical results are demonstrated by numerical simulations.

Depending on behavioral differences, reproductive capability and dependency, the life span of a species is divided mainly into two classes, namely immature and mature. In this paper, we have studied the dynamics of a predator–prey system considering stage structure in prey and the effect of predator-induced fear with two discrete time delays: maturation delay and fear response delay. We consider that predators cooperate during hunting of mature prey and also include its impact in fear term. The conditions for existence of different equilibria, their stability analysis are carried out for non-delayed system and bifurcation results are presented extensively. It is observed that the fear parameter has stabilizing effect whereas the cooperative hunting factor having destabilizing effect on the system via occurrence of supercritical Hopf-bifurcation. Further, we observe that the system exhibits backward bifurcation between interior equilibrium and predator free equilibrium and hence the situation of bi-stability occurs in the system. Thereafter, we differentiate the region of stability and instability in bi-parametric space. We have also studied the system’s dynamics with respect to maturation and fear response delay and observed that they also play a vital role in the system stability and occurrence of Hopf-bifurcation is shown with respect to both time delays. The system shows stability switching phenomenon and even higher values of fear response delay leads the system to enter in chaotic regime. The role of fear factor in switching phenomenon is discussed. Comprehensive numerical simulation and graphical presentation are carried out using MATLAB and MATCONT.

In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô${}^{\prime }s$ formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.

Connectivity analysis using modern approaches like Granger causality, partial directed coherence and transfer entropy always demands additional statistical evaluation of the obtained measures for significance. Although for very simple linear autoregressive processes and quasilinear oscillatory activities theoretical estimates are available, the real biological signals are too complex for application of analytical approaches and surrogate data come into use. When pathological activity like epileptic seizures is studied, the question can also rise in a somewhat different way: one asks whether the studied activity is different from the normal one rather than whether connectivity exists. The similar question is also valid if one compares connectivity in different physiological states like sleep and wakefulness.

Here, we study two different approaches to statistical evaluation of transfer entropy estimates in application to the study of spike–wave discharges (SWDs), the main encephalographic manifestation of absence epilepsy, registered in local field potentials of WAG/Rij rats (genetic models). The first approach is to compare distributions of the estimators for the baseline and different stages of pathological activity using traditional measures like t-test with additional corrections for multiple testing. The second approach is to make surrogate data and test whether the achieved estimators differ for surrogate series and for real ones. To support our findings and to understand the methods better, the series simulated using simple oscillatory models of epileptic activity are evaluated in the same way as the experimental data.

We show that the most pronounced phenomena like bidirectional increase in coupling between frontal and parietal cortical areas during SWDs in comparison to baseline activity are considered to be significant by both approaches. But when the less expressed coupling changes are under consideration, the approach base on surrogate data provides less false positives. These results confirm that the primary outcomes of connectivity analysis for absence epilepsy (and not only it) achieved previously are valid although the statistical evaluation of the connectivity estimators was suboptimal.

We propose and study the transmission dynamics of susceptible-exposed-infected-recovered $(XYZW)$ epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It$ô$’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.

We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number ${\Re }_0$ is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when ${\Re }_0<1$, and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when ${\Re }_0>1$. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.