International Journal of Biomathematics

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

In this paper, a fractional order model of the phytoplankton–toxic phytoplankton–zooplankton system with Caputo fractional derivative is investigated via three computational methods, namely, residual power series method (RPSM), homotopy perturbation Sumudu transform method (HPSTM) and the homotopy analysis Sumudu transform method (HASTM). This model is constituted by three components: phytoplankton, toxic phytoplankton and zooplankton. Phytoplankton species are self-feeding members of the plankton community and play a very significant role in ecosystems. A wide range of sea creatures get food through phytoplankton. This paper focuses on the implementation of the three above-mentioned computational methods for a nonlinear time-fractional phytoplankton–toxic phytoplankton–zooplankton (PTPZ) model with a perception to study the dynamics of a model. This study shows that the solutions obtained by employing the suggested computational methods are in good agreement with each other. The computational procedures reveal that the HASTM solution generates a more general solution as compared to RPSM and HPSTM and incorporates their results as a special case. The numerical results presented in the form of graphs authenticate the accuracy of computational schemes. Hence, the implemented methods are very appropriate and relevant to handle nonlinear fractional models. In addition, the effect of variation of fractional order of a time derivative and time $t$ on populations of phytoplankton, toxic–phytoplankton and zooplankton has also been studied through graphical presentations. Moreover, the uniqueness and convergence analyses of HASTM solution have also been discussed in view of the Banach fixed-point theory.

H7N9 avian influenza is a highly pathogenic zoonotic disease. In order to control the disease, many strategies have been adopted in China such as poultry culling, the closure of live poultry markets (LPMs), the vaccination of poultry, and the treatment for humans. Due to the limited resource, it is of paramount significance to achieve the optimal control. In this paper, an epidemic model incorporating the selective culling rate is formulated to investigate the transmission mechanism of H7N9. The threshold dynamics and bifurcation analyses of the model are well investigated. Furthermore, the problem of optimal control is explored in line with Pontryagin’s Maximum Principle, with consideration given to the comprehensive measures. The numerical simulations suggest that the vaccination of poultry and the closure of LPMs are the two most economical and effective measures.

In this paper, a predator–prey reaction–diffusion model with Rosenzweig–MacArthur type functional response and spatiotemporal delay is investigated through using the tool of Turing bifurcation theories. First, by taking the average time delay as a bifurcation parameter, conditions of occurrence of Turing bifurcation are obtained through employing the Routh–Hurwitz criteria. Second, as the average time delay varies the amplitude equations of Turing bifurcation patterns including spots pattern and stripes pattern are also obtained through the multiple scale perturbation method. Finally, the two kinds of spatiotemporal evolution distributions of species such as spots pattern and stripes pattern are shown to illustrate theoretical results.

In this paper, we explore the local dynamical behavior with different topological classifications around fixed points, Neimark–Sacker bifurcation and hybrid control in the discrete-time Phytoplankton–Zooplankton model. More precisely, we have investigated the local dynamical behavior with different topological classifications around trivial, semitrivial and interior fixed points of the two-dimensional Phytoplankton–Zooplankton model, respectively. The existence of possible bifurcations around fixed points is also investigated, and it is proved that there exists no flip bifurcation around trivial and semitrivial fixed points but around interior fixed point, the model undergoes Neimark–Sacker bifurcation only. Moreover, hybrid control strategy is utilized for controlling Neimark–Sacker bifurcation in the Phytoplankton–Zooplankton model. Lastly, theoretical results are verified numerically.

The main aim of this paper is to study the dynamics of a recurrent neural networks with different input currents in terms of asymptotic point. Under certain circumstances, we studied the existence, the uniqueness of bounded solutions and their homoclinic and heteroclinic motions of the considered system with rectangular currents input. Moreover, we studied the unpredictable behavior of the continuous high-order recurrent neural networks and the discrete high-order recurrent neural networks. Our method was primarily based on Banach’s fixed-point theorem, topology of uniform convergence on compact sets and Gronwall inequality. For the demonstration of theoretical results, we give examples and their numerical simulations.

In this paper, we consider five mathematical models of corona virus infection. The first model is a mathematical model of corona virus entry. The second model is a mathematical model for interactions of virus N-protein and viral RNA. Here, we prove that phosphorylated N protein increases the affinity of viral RNA. The third model is a mathematical model of virion assembly. It is a six-dimensional model. But there is an invariant three-dimensional submodel, which we can prove has a positive stable equilibrium. The fourth model is a model of an enzyme inhibitor that blocks viral replication. The fifth model is a model of a virus and a vaccine.

The aim of this work is to present a design of Morlet wavelet neural network (MWNN) for solving a novel prevention category (P) in the HIV system, known as HIPV mathematical model. The numerical performance of the novel HIPV mathematical model will be observed by exploiting the MWNN that works through the optimization procedures of global/local via “genetic algorithm (GA)” and local search “interior-point algorithm (IPA)”, i.e. MWNN-GA-IPA. An error function using the differential HIPV mathematical model and its initial conditions is presented and optimized by the MWNN-GA-IPA. The obtained results have been compared with the Adams method to check the competence of the MWNN-GA-IPA. For the reliability and stability of the scheme, the performance using different statistical operators has been performed based on the multiple independent trials to solve the novel HIPV mathematical model.

It is well known that some enzymes, proteins, amino-acids between other biological molecules have more than one way to be coded in the DNA. That means, there are some biological molecules that can be identified by a set of sequences. For instance, the enzyme SmaI can be recognized by the words $CCCGGG$ and $GGGCCC$. In this paper, we count the number of times that a biological sequence occurs through the DNA by any of its configurations, i.e. we provide the strong law of large numbers for a word sequence. To achieve our goal, we consider that DNA is modeled by an ergodic semi-Markov chain. We also present the Central Limit Theorem. Additionally, we compute the first hitting position of a set of words.

This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely $x$ and $y$, and the third species $z$ behaves as the predator and also host for $x$. The species $z$ predating on the species $y$ with the Holling type-II functional response, while the first species $x$ is benefited from the third species $z$. Further, the effect of fear is incorporated in the growth rate of species $x$ due to the predator $y$ and time lag in $z$ due to the gestation process. We explore all the biologically possible equilibrium points, and their local stability is analyzed based on the sample parameters. Next, we investigate the occurrence of Hopf-bifurcation around the interior equilibrium point by taking the value of the fear parameter as a bifurcation parameter for the non-delayed system. Moreover, we verify the local stability and existence of Hopf-bifurcation for the corresponding delayed system. Also, the direction and stability of the bifurcating periodic solutions are determined using the normal form theory and the center manifold theorem. Finally, we perform extensive numerical simulations to support the evidence of our analytical findings.

The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

In this paper, we study the traveling wave problem for a three species lattice competition system with monostable nonlinearity. We are interested in the linear or nonlinear determinacy of the minimal wave speed. Some conditions on the linear determinacy has been obtained in [J.-S. Guo, Y. Wang, C.-H. Wu and C.-C. Wu, The minimal speed of traveling wave solutions for a diffusive three species competition system, Taiwanese J. Math. 19 (2015) 1805–1829]. In this paper, we first provided some general conditions for the linear determinacy. Then, we derive some novel results on the nonlinear determinacy. Finally, some numerical simulations are carried out to illustrate our analytic results. To our knowledge, this may be the first investigation on the nonlinear determinacy of the three species competition system.