Journal of Biological Dynamics最新文献

Latently infected CD$4^{+}$ T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs.

In this work, we consider a chaotic system that plays a vital role in the treatment of cancer by injection of a virus externally. Due to the sensitivity of this disease, most of its treatments are highly risky. Therefore, we have designed control inputs using adaptive and passive control techniques for virotherapy. Both controllers are designed to bring global stability to the cancer system with the aid of a quadratic Lyapunov function. Furthermore, we use simulations to verify our controllers. Moreover, we show that our adaptive control technique gives better results in comparison.

Which reduced-mixing strategy maximizes economic output during a disease outbreak? To answer this question, we formulate an optimal-control problem that maximizes the difference between revenue, due to healthy individuals, and medical costs, associated with infective individuals, for SIS disease dynamics. The control variable is the level of mixing in the population, which influences both revenue and the spread of the disease. Using Pontryagin's maximum principle, we find a closed-form solution for our problem. We explore an example of our problem with parameters for the transmission of Staphylococcus aureus in dairy cows, and we perform sensitivity analyses to determine how model parameters affect optimal strategies. We find that less mixing is preferable when the transmission rate is high, the per-capita recovery rate is low, or when the revenue parameter is much smaller than the cost parameter.

The cross-border mobility of malaria cases poses an obstacle to malaria elimination programmes in many countries, including Nepal. Here, we develop a novel mathematical model to study how the imported malaria cases through the Nepal-India open-border affect the Nepal government's goal of eliminating malaria by 2026. Mathematical analyses and numerical simulations of our model, validated by malaria case data from Nepal, indicate that eliminating malaria from Nepal is possible if strategies promoting the absence of cross-border mobility, complete protection of transmission abroad, or strict border screening and isolation are implemented. For each strategy, we establish the conditions for the elimination of malaria. We further use our model to identify the control strategies that can help maintain a low endemic level. Our results show that the ideal control strategies should be designed according to the average mosquito biting rates that may depend on the location and season.

Based on evolutionary game theory and Darwinian evolution, we propose and study discrete-time competition models of two species where at least one species has an evolving trait that affects their intra-specific, but not their inter-specific competition coefficients. By using perturbation theory, and the theory of the limiting equations of non-autonomous discrete dynamical systems, we obtain global stability results. Our theoretical results indicate that evolution may promote and/or suppress the stability of the coexistence equilibrium depending on the environment. This relies crucially on the speed of evolution and on how the intra-specific competition coefficient depends on the evolving trait. In general, equilibrium destabilization occurs when $\alpha >2$, when the speed of evolution is sufficiently slow. In this case, we conclude that evolution selects against complex dynamics. However, when evolution proceeds at a faster pace, destabilization can occur when $\alpha <2$. In this case, if the competition coefficient is highly sensitive to changes in the trait v, destabilization and complex dynamics occur. Moreover, destabilization may lead to either a period-doubling bifurcation, as in the non-evolutionary Ricker equation, or to a Neimark-Sacker bifurcation.

In this paper, we derive a delayed epidemic model to describe the characterization of cytotoxic T lymphocyte (CTL)-mediated immune response against virus infection. The stability of equilibria and the existence of Hopf bifurcation are analysed. Theoretical results reveal that if the basic reproductive number is greater than 1, the positive equilibrium may lose its stability and the bifurcated periodic solution occurs when time delay is taken as the bifurcation parameter. Furthermore, we investigate an optimal control problem according to the delayed model based on the available therapy for hepatitis B infection. With the aim of minimizing the infected cells and viral load with consideration for the treatment costs, the optimal solution is discussed analytically. For the case when periodic solution occurs, numerical simulations are performed to suggest the optimal therapeutic strategy and compare the model-predicted consequences.

We investigate a mosquito population suppression model, which includes the release of Wolbachia-infected males causing incomplete cytoplasmic incompatibility (CI). The model consists of two sub-equations by considering the density-dependent birth rate of wild mosquitoes. By assuming the release waiting period T is larger than the sexual lifespan $\overline{T}$ of Wolbachia-infected males, we derive four thresholds: the CI intensity threshold $s_h^{\ast }$, the release amount thresholds $g^{\ast }$ and $c^{\ast }$, and the waiting period threshold $T^{\ast }$. From a biological view, we assume $s_h>s_h^{\ast }$ throughout the paper. When $g^{\ast }<c<c^{\ast }$, we prove the origin $E_0$ is locally asymptotically stable iff $T<T^{\ast }$, and the model admits a unique T-periodic solution iff $T\ge T^{\ast }$, which is globally asymptotically stable. When $c\ge c^{\ast }$, we show the origin $E_0$ is globally asymptotically stable iff $T\le T^{\ast }$, and the model has a unique T-periodic solution iff $T>T^{\ast }$, which is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations.

In this paper, the invasive speed selection of the monostable travelling wave for a three-component lattice Lotka-Volterra competition system is studied via the upper and lower solution method, as well as the comparison principle. By constructing several special upper and lower solutions, we establish sufficient conditions such that the linear or nonlinear selection is realized.

In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay τ as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such a random network nutrient-microorganism model. Noticing that the results of the direction of the Hopf bifurcation in a random network model are rare, we thus try to use the method of multiple time scales (MTS) to derive amplitude equation and determine the direction of the Hopf bifurcation. It is showed that the delayed random network nutrient-microorganism model can exhibit a supercritical or subcritical Hopf bifurcation. Numerical experiments are performed to verify the validity of the theoretical analysis.

The goal of this paper is to investigate the influence of the waning immunity on the dynamics of Tilapia Lake Virus (TiLV) transmission in wild and farmed tilapia within freshwater. We formulate a model for which susceptible individuals can contract the disease in two ways: (i) direct mode caused by contact with infected individuals; (ii) indirect mode due to the presence of pathogenic agents in the water. We obtain an age-structured model which combines both age since infection and age since recovery. We derive an explicit formula for the reproductive number $R_0$ and show that the disease-free equilibrium is locally asymptotically stable when, $R_0<1$. We discuss on the form of the waning immunity parameter and show numerically that a Hopf bifurcation may occur for suitable immunity parameter values, which means that there is a periodic solution around the endemic equilibrium when, $R_0>1$.