International Journal of Biomathematics

In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.

This paper considers a novel distributed order time fractional dual-phase-lag model to analyze the anomalous diffusion in a comb structure, which has a widespread application in medicine and biology. The newly proposed constitution model is a generalization of the dual-phase-lag model, in which a spectrum of the time fractional derivatives with the memory characteristic governed by the weight coefficient is considered and the formulated governing equation contains both the diffusion and wave characteristics. With the L1-formula to discrete the time Caputo fractional derivatives, the finite difference method is used to discretize the model and the related numerical results are plotted graphically. By adding a source term, an exact solution is defined to verify the correctness of the numerical scheme and the convergence order of the error in spatial direction is presented. Finally, the dynamic characteristics of the particle distributions and the effects of involved parameters on the total number of particles in the $x$-direction are analyzed in detail.

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled.

Innovative and astonishing developments in the field of spine analysis can commence with this manuscript. The lumbar disks ($L1-L2$ to $L5-S1$) are most commonly impaired by degeneration due to their long-standing degeneration and associated strain. We investigate the indications, purposes, risk factors, and therapies of lumbar degenerated disc disease (L-DDD). We assume that the degeneration of five discs creates many effects, making it difficult to differentiate between the different types of degenerated discs and their seriousness. Since the indeterminacy and falsity portions of science or clinical diagnosis are often ignored. Due to this complexity, the reliability of the patient’s progress report cannot be calculated, nor can the period of therapy be measured. The revolutionary concept of interval-valued m-polar neutrosophic Choquet integral aggregation operator (IVmPNCIAO) is proposed to eliminate these problems. We associate generalized interval-valued m-polar neutrosophic Choquet integral aggregation operator (GIVmPNCIAO) with the statistical formulation of $L^p$-spaces and use it to identify the actual kind of degenerative disc in the lumbar spine. For the classification of interval-valued m-polar neutrosophic numbers (IVMPNNs), we set the ranking index and score function. These concepts are appropriate and necessary in order to better diagnose degeneration by associating it with mathematical modeling. We construct a pre-diagnosis map based on the fuzzy interval $[0,1]$ to classify the types of degenerative discs. We develop an algorithm by using GIVmPNCIAO based on interval-valued m-polar neutrosophic sets (IVMPNNs) to identify the degenerative disc appropriately and to choose the most exquisite treatment for the corresponding degeneration of every patient. Furthermore, we discuss the sensitivity analysis with parameter $p$ in GIVmPNCIAO to investigate the patient’s improvement record.

The paper investigates the existence of a relationship between the diapause duration and the temperature threshold of hatching, the variances in temperature and hatching time of the artificial six-month population of Lymantria dispar caterpillars. A half-year population gives two generations a year under artificial conditions. A comparative analysis of these parameters with similar parameters of the hybrid population of L. dispar, as well as studies by other authors, has been carried out. The Eigen quasispecies model was used for the mathematical formalization of the evolution process. The results of this work can be used to study the evolution of L. dispar.

In this paper, we study the dynamical behavior of a stochastic two-compartment model of $B$-cell chronic lymphocytic leukemia, which is perturbed by white noise. Firstly, by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then, conditions for extinction of the disease are derived. Furthermore, numerical simulations are presented for supporting the theoretical results. Our results show that large noise intensity may contribute to extinction of the disease.

Dengue is among the most important infectious diseases in the world. The main contribution of our paper is to present a mixed system of partial and ordinary differential equations. This combined model is a generalization of the two presented mathematical models (A. L. de Araujo, J. L. Boldrini and B. M. Calsavara, An analysis of a mathematical model describing the geographic spread of dengue disease, J. Math. Anal. Appl. 444 (2016) 298–325) and (L. Cai, X. Li, N. Tuncer, M. Martcheva and A. A. Lashari, Optimal control of a malaria model with asymptomatic class and superinfection, Math. Biosci. 288 (2017) 94–108), describing the geographic spread of dengue disease. Our model has the ability to consider the possibility of asymptomatic infection, which leads to investigate the effect of dengue asymptomatic individuals on disease dynamics and to go into the possibility of superinfection of asymptomatic individuals. In the light of considering these factors, as well as the movements of human and mature female mosquitoes, more realistic modeling of dengue disease can be achieved. We present a mathematical analysis and show the global existence of a unique non-negative solution to this model and then establish ways to control dengue disease using numerical simulations and sensitivity analysis of model parameters (which are related to the contact rates and death rate of winged mosquitoes). To show different biological behaviors, we provide several numerical results, showing the role of parameters in controlling dengue disease transmission. From our numerical simulations, it can also be concluded that local control of dengue transmission can be done at a lower cost.

The study examines the population-level impact of temperature variability and immigration on malaria prevalence in Nigeria, using a novel deterministic model. The model incorporates disease transmission by immigrants into the community. In the absence of immigration, the model is shown to exhibit the phenomenon of backward bifurcation. The disease-free equilibrium of the autonomous version of the model was found to be locally asymptotically stable in the absence of infective immigrants. However, the model exhibits an endemic equilibrium point when the immigration parameter is greater than zero. The endemic equilibrium point is seen to be globally asymptotically stable in the absence of disease-induced mortality. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to malaria transmission dynamics in Nigeria, shows that the top three parameters that drive malaria prevalence (with respect to ${{ℛ}}_0$) are the mosquito natural death rate (${\mu }_M$), mosquito biting rate ($b_M$) and the transmission rates between humans and mosquitoes (${\beta }_H,{\beta }_M$). Numerical simulations of the model show that in Nigeria, malaria burden increases with increasing mean monthly temperature in the range of 22–28${}^{\circ }\mathrm{\text{C}}$. Thus, this study suggests that control strategies for malaria should be intensified during this period. It is further shown that the proportion of infective immigrants has marginal effect on the transmission dynamics of the disease. Therefore, the simulations suggest that a reduction in the fraction of infective immigrants, either exposed or infectious, would significantly reduce the malaria incidence in a population.

In this paper, we use a semidiscretization method to derive a discrete predator–prey model with Holling type II, whose continuous version is stated in [F. Wu and Y. J. Jiao, Stability and Hopf bifurcation of a predator-prey model, Bound. Value Probl. 129 (2019) 1–11]. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Then we obtain the sufficient conditions for the occurrence of the transcritical bifurcation and Neimark–Sacker bifurcation and the stability of the closed orbits bifurcated by using the Center Manifold theorem and bifurcation theory. Finally, we present numerical simulations to verify corresponding theoretical results and reveal some new dynamics.

Approximation space can be said to play a critical role in the accuracy of the set’s approximations. The idea of “approximation space” was introduced by Pawlak in 1982 as a core to describe information or knowledge induced from the relationships between objects of the universe. The main objective of this paper is to create new types of rough set models through the use of different neighborhoods generated by a binary relation. New approximations are proposed representing an extension of Pawlak’s rough sets and some of their generalizations, where the precision of these approximations is substantially improved. To elucidate the effectiveness of our approaches, we provide some comparisons between the proposed methods and the previous ones. Finally, we give a medical application of lung cancer disease as well as provide an algorithm which is tested on the basis of hypothetical data in order to compare it with current methods.

In this paper, we propose a reaction–diffusion viral infection model with nonlinear incidences, cell-to-cell transmission, and a time delay. We impose the homogeneous Neumann boundary condition. For the case where the domain is bounded, we first study the well-posedness. Then we analyze the local stability of homogeneous steady states. We establish a threshold dynamics which is completely characterized by the basic reproduction number. For the case where the domain is the whole Euclidean space, we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder’s fixed point theorem. Finally, we study how the speed of spread in space affects the spread of cells and viruses. We obtain the existence of the wave speed, which is dependent on the diffusion coefficient.