International Journal of Biomathematics

We propose a modified discrete-time Leslie–Gower competition system of two populations to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar competitive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.

In this paper, we propose a non-autonomous convection–reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. The main contributions of this paper are: (i) the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system (CDI)_e, (ii) sufficient conditions for the existence of a positive solution of (CDI)_e based on the Leray–Schauder’s degree theory. Numerical simulations which support our theoretical analysis are also given.

We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton–Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.

In this paper, we consider a diffusive density-dependent predator–prey model with Crowley–Martin functional responses subject to Neumann boundary condition. We analyze the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through the distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally, numerical simulations are given to verify our theoretical analysis.

In this paper, two delay differential systems are considered, namely, a famous model from mathematical biology about the spread of HIV viruses in blood and the advanced Lorenz system from mathematical physics. We then apply the homotopy perturbation method (HPM) to find their approximate solutions. It turns out that the method gives rise to easily obtainable solutions. In addition, residual error functions of the solutions are graphed and it is shown that increasing the parameter $n$ in the method improves the results in both cases.

In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number ${{ℛ}}_0$. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder’s fixed point theorem and the limiting arguments, we show that when ${{ℛ}}_0>1$, there exists a constant $c^{\ast }>0$ such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for $c>c^{\ast }$, and when ${{ℛ}}_0>1$ and $c<c^{\ast }$, the model has no positive traveling wave solutions connecting them.

In this paper, a three-species system consisting of two predators which are in mutualism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey–predator system are considered. So the biological parameters are not precise in reality. This paper presents a different approach to study the prey–predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under impreciseness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin’s maximum principle. Numerical examples are provided to support the proposed approach.

We formulate an age-structured model based on a system of nonlinear partial differential equations to assist the early and catch up female vaccination programs for human papillomavirus (HPV) types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible (SIS) structure. We calculate the effective reproduction number $R_v$ for the model and describe the local-asymptotic stability of the disease-free equilibrium using $R_v$. We prove the existence of an endemic equilibrium for $R_v>1$ for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.

The use of cholera vaccines has been increasingly recognized as an effective control measure in cholera endemic countries. Also, the disease transmissions are getting more complicated and thus comprehensive strategies to implement public health control measures are worthwhile to be investigated. In this paper, we aim to better understand the effects of HI states of vibrios from the environment and from human contacts that cause cholera outbreaks. We also present and analyze our cholera mathematical model with vaccine incorporated. Equilibrium analysis is conducted in the case with constant control for both epidemic and endemic dynamics. Optimal control theory is applied to seek cost-effective solutions of time-dependent vaccination strategies against cholera outbreaks. Our results show that using vaccination during cholera outbreaks at the very beginning of the onset can reduce the number of infections significantly.

Revolutionary in scope and application, the CRISPR Cas9 endonuclease system can be guided by 20-nt single guide RNA (sgRNA) to any complementary loci on the double-stranded DNA. Once the target site is located, Cas9 can then cleave the DNA and introduce mutations. Despite the power of this system, sgRNA is highly susceptible to off-target homologous attachment and can consequently cause Cas9 to cleave DNA at off-target sites. In order to better understand this flaw in the system, the human genome and Streptococcus pyogenes Cas9 (SpCas9) were used in a mathematical and computational study to analyze the probabilities of potential sgRNA off-target homologies. It has been concluded that off-target sites are nearly unavoidable for large-size genomes, such as the human genome. Backed by mathematical analysis, a viable solution is the double-nicking method which has the promise for genome editing specificity. Also applied in this study was a computational algorithm for off-target homology search that was implemented in Java to confirm the mathematical analysis.

The purpose of this paper is to study the traveling wave solutions of a diffusive predator–prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibrium $E_0$, a boundary equilibrium $E_1$ and a positive equilibrium $E_{\ast }$ under some conditions. We establish the existence of two types of traveling wave solutions which connect $E_0$ and $E_{\ast }$ and $E_1$ and $E_{\ast }$, respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investigate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.

Chikungunya and dengue viruses are transmitted by mosquitoes of genus Aedes. Based on a mathematical model dealing with arboviruses transmission that encompasses human and mosquito populations, the risks of dengue and chikungunya infections are compared. By the fact that chikungunya virus attains high viral load earlier than dengue virus in both humans and mosquitoes, the potential risk of chikungunya could be higher than the dengue infection. The risk of arboviruses infections is assessed by the reproduction number $R$, which is obtained by the next generation matrix method and Routh–Hurwitz criteria.

Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed including cross-protection. Global dynamics of the model was discussed. Under the quite weak assumptions, integral form conditions were resolved for permanence of the system and extinction of diseases. Furthermore, we looked into the sufficient conditions that plants could be protected against the detrimental effects of infection by an infection with the mild virus isolates. Last, we performed numerical simulations. Our investigations suggested that cross-protection played an important role in controlling the spread of the challenging virus in plants.

A two-parameter family of discrete models, consisting of two coupled nonlinear difference equations, describing a host–parasite interaction is considered. In particular, we prove that the model has at most one nontrivial interior fixed point which is stable for a certain range of parameter values and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter.

The purpose of this work is to investigate the asymptotic properties of a stochastic Gilpin–Ayala population system under regime switching on patches. We establish the global stability and the extinction of the trivial equilibrium state of the model. Furthermore, we show the existence of the stationary distribution for our system model. The analytical results are illustrated by computer simulations.