International Journal of Biomathematics

In this paper, we have analyzed a tri-trophic food chain model consisting of phytoplankton, zooplankton and fish population in an aquatic environment. Here, the pelagic water column is divided into two layers namely, the upper layer and the lower layer. The zooplankton population makes a diel vertical migration (DVM) from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator (Fish). Here, mathematical model has been developed and analyzed in a rigorous way. Apart from routine calculations like boundedness and positivity of the solution, local stability of the equilibrium points, we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way. It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system. Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation. The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system, whereas the downward migration rate enhance the stability of the system. Further, we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations. We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible. Finally, extensive numerical simulation has been performed to support our analytical findings.

In this paper, we study a class of singular stochastic bio-economic models described by differential-algebraic equations due to the influence of economic factors. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. Stochastic stability and Hopf bifurcations can be analytically determined based on the singular boundary theory of diffusion process, the Maximal Lyapunov exponent and the invariant measure theory. The critical value of the stochastic Hopf bifurcation parameter is obtained and the position of Hopf bifurcation drifting with the parameter increase is presented as a result. Practical example is presented to verify the effectiveness of the results.

In this paper, we define a new idea of trapezoidal neutrosophic cubic hesitant fuzzy number based on migraine diseases. We define and the migraine diseases on trapezoidal neutrosophic cubic hesitant fuzzy number and operational laws of trapezoidal neutrosophic cubic hesitant fuzzy number and hamming distance of TrNCHFNs. The new concept of trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method is introduced. Furthermore, we extend MCDM method based on the trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method.

In many medical researches, it is needed to determine the optimal sample size allocation in a heterogeneous population. This paper proposes the algorithm for optimal sample size allocation. We consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection, Secant, Regula–Falsi and other numerical methods. The performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time, number of iterations and gain in accuracy using stratification. The efficacy of algorithm is evaluated for the response in terms of body mass index (BMI) to the dietetic supplement with diabetes mellitus, HIV/AIDS and cancer post-operatory recovery patients.

Malaria infection continues to be a major problem in many parts of the world including Africa. Environmental variables are known to significantly affect the population dynamics and abundance of insects, major catalysts of vector-borne diseases, but the exact extent and consequences of this sensitivity are not yet well established. To assess the impact of the variability in temperature and rainfall on the transmission dynamics of malaria in a population, we propose a model consisting of a system of non-autonomous deterministic equations that incorporate the effect of both temperature and rainfall to the dispersion and mortality rate of adult mosquitoes. The model has been validated using epidemiological data collected from the western region of Ethiopia by considering the trends for the cases of malaria and the climate variation in the region. Further, a mathematical analysis is performed to assess the impact of temperature and rainfall change on the transmission dynamics of the model. The periodic variation of seasonal variables as well as the non-periodic variation due to the long-term climate variation have been incorporated and analyzed. In both periodic and non-periodic cases, it has been shown that the disease-free solution of the model is globally asymptotically stable when the basic reproduction ratio is less than unity in the periodic system and when the threshold function is less than unity in the non-periodic system. The disease is uniformly persistent when the basic reproduction ratio is greater than unity in the periodic system and when the threshold function is greater than unity in the non-periodic system.

In this paper, we establish the existence of local stable manifolds for a semi-linear differential equation, where the linear part is a Hille–Yosida operator on a Banach space and the nonlinear forcing term $f$ satisfies the $\phi$-Lipschitz conditions, where $\phi$ belongs to certain classes of admissible function spaces. The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.

This paper investigates behaviors that a set of initial cell densities of Heterocapsa Circularisquama (HC) and Prorocentrum Dentatum (PD) and a set of environmental factors disturbing the growth of HC and PD cells formed in their growth process, which are actually fractal phenomena. First, the calculation of the fractal dimension of the set of initial cell densities of HC and PD is given in the paper. Second, by controlling the set of initial cell density, HC and PD cells grow according to a given growth target. The approximate or same behaviors of two different sets of initial cell densities of HC and PD are realized by introducing the coupling terms. Finally, the set of environmental factors disturbing the growth of HC and PD cells is constructed by introducing real parameters. Then the result that makes HC and PD cells growing according to a given growth target is reached by a proper mathematical transform to the real parameters. The approximate or same behaviors of the set of environmental factors disturbing the growth of HC and PD cells are realized by introducing the coupling terms.

We investigate an optimal harvesting problem for age-structured species, in which elder individuals are more competitive than younger ones, and the population is modeled by a highly nonlinear integro-partial differential equation with a global feedback boundary condition. The existence of optimal strategies is established by means of compactness and maximizing sequences, and the maximum principle obtained via an adjoint system, tangent-normal cones and a new continuity result. In addition, some numerical experiments are presented to show the effects of the price function and younger’s weight on the optimal profits.

A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper. We introduce the basic reproduction number ${{ℛ}}_0$ first. Then the existence of endemic equilibrium (EE) can be determined by the sizes of ${{ℛ}}_0$ as well as the diffusion rates of susceptible and infected individuals. We also investigate the effect of diffusion rates on asymptotic profile of EE. Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population $N$ is below a certain level; while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.