Journal of Biological Dynamics最新文献

Outbreaks of highly pathogenic strains of avian influenza (HPAI) cause high mortality in avian populations worldwide. When spread from avian reservoirs to humans, HPAI infections cause mortality in about 50% of human infections. Cases of human-to-human transmission of HPAI are relatively rare, and have, to date, only been reported in situations of close contact. These transmissions have resulted in isolated clusters of human HPAI infections, but have not yet caused a pandemic. Given the large number of human H5N1 HPAI infections to date, none of which has resulted in a pandemic, we estimate an upper bound on the probability of H5N1 pandemic emergence. We use this estimate to provide the likelihood of observing such a pandemic over the next decade. We then develop a more accurate parameter-based estimate of the emergence probability and predict the likelihood that, through rare mutations, an H5N1 influenza pandemic will emerge over the same time span.

Pest control based on an economic threshold (ET) can effectively prevent excessive pest control measures such as pesticide abuse and overharvesting. The instinctive dispersal of pest populations in biological network patches for better survival poses challenges for pest management. As long as the pest density is controlled below the economic threshold and no pest outbreak occurs, the aim of pest management can be achieved and it is not necessary to completely remove the pests. This study focuses on the issues of chimera states and cluster solutions in regular bidirectional biological networks with state-dependent impulsive pest management. We consider the influence of two different control modes on the system states, namely global control and local control. Local control is found to be more likely to induce the chimera state. In addition, in the local coupling mode, a higher coupling strength is more likely to generate a coherent state, whereas a lower coupling strength is more likely to generate chimera and incoherent states. Furthermore, the cluster size is inversely related to the coupling strength under local coupling and global control.

The coronavirus disease 2019 (COVID-19) remains a global pandemic at present. Although the human-to-human transmission route for this disease has been well established, its transmission mechanism is not fully understood. In this paper, we propose a mathematical model for COVID-19 which incorporates multiple transmission pathways and which employs time-dependent transmission rates reflecting the impact of disease prevalence and outbreak control. Applying this model to a retrospective study based on publicly reported data in China, we argue that the environmental reservoirs play an important role in the transmission and spread of the coronavirus. This argument is supported by our data fitting and numerical simulation results for the city of Wuhan, for the provinces of Hubei and Guangdong, and for the entire country of China.

The well known linear chain trick (LCT) allows modellers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these sub-states is the sum of k exponentially distributed random variables, and is thus gamma distributed. The generalized linear chain trick (GLCT) extends this technique to the broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Phase-type distributions are the family of matrix exponential distributions on $[0,\infty )$ that represent the absorption time distributions for finite-state, continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build ODE models from underlying stochastic model assumptions. We introduce two novel model families by using the GLCT to generalize the Rosenzweig-MacArthur predator-prey model, and the SEIR model. We illustrate the kinds of complexity that can be captured by such models through multiple examples. We also show the benefits of using a GLCT-based model formulation to speed up the computation of numerical solutions to such models. These results highlight the intuitive nature, and utility, of using the GLCT to derive ODE models from first principles.

Drugs of abuse, such as opiates, are one of the leading causes for transmission of HIV in many parts of the world. Drug abusers often face a higher risk of acquiring HIV because target cell (CD4+ T-cell) receptor expression differs in response to morphine, a metabolite of common opiates. In this study, we use a viral dynamics model that incorporates the T-cell expression difference to formulate the probability of infection among drug abusers. We quantify how the risk of infection is exacerbated in morphine conditioning, depending on the timings of morphine intake and virus exposure. With in-depth understanding of the viral dynamics and the increased risk for these individuals, we further evaluate how preventive therapies, including pre- and post-exposure prophylaxis, affect the infection risk in drug abusers. These results are useful to devise ideal treatment protocols to combat the several obstacles those under drugs of abuse face.

In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of $R^n$ with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level $R_0\le 1,$ the disease-free equilibrium $E_0$ is globally asymptotically stable. On the other hand, if $R_0>1$ then there exists a unique stable disease equilibrium $E^{\ast }$. The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value $R_0$.

Here we present a novel application of stage-structured population modelling to explore the properties of neuronal dendrites with spines. Dendritic spines are small protrusions that emanate from the dendritic shaft of several functionally important neurons in the cerebral cortex. They are the postsynaptic sites of over 90% of excitatory synapses in the mammalian brain. Here, we formulate a stage-structured population model of a passive dendrite with activity-dependent spines using a continuum approach. This computational study models three dynamic populations of activity-dependent spine types, corresponding to the anatomical categories of stubby, mushroom, and thin spines. In this stage-structured population model, transitions between spine type populations are driven by calcium levels that depend on local electrical activity. We explore the influence of the changing spine populations and spine types on the development of electrical propagation pathways in response to repetitive synaptic input, and which input frequencies are best for facilitating these pathways.

In this paper, we use an adaptive modeling framework to model and study how nutritional status (measured by the protein to carbohydrate ratio) may regulate population dynamics and foraging task allocation of social insect colonies. Mathematical analysis of our model shows that both investment to brood rearing and brood nutrition are important for colony survival and dynamics. When division of labour and/or nutrition are in an intermediate value range, the model undergoes a backward bifurcation and creates multiple attractors due to bistability. This bistability implies that there is a threshold population size required for colony survival. When the investment in brood is large enough or nutritional requirements are less strict, the colony tends to survive, otherwise the colony faces collapse. Our model suggests that the needs of colony survival are shaped by the brood survival probability, which requires good nutritional status. As a consequence, better nutritional status can lead to a better survival rate of larvae and thus a larger worker population.

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two Streptococcus pneumoniae (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA. The model, which is rigorously analysed to investigate the existence and asymptotic stability properties of the associated equilibria (in addition to exploring conditions for competitive exclusion), is simulated to assess the impact of vaccination under different levels of serotype-specific competition and illustrate the phenomenon of serotype replacement. The calibrated model is used to forecast the carriage prevalence in the pediatric cohort over 30 years.

Previous works using different mathematical techniques, however, show that the concavity of the trade-off relationship can alter the expected life history strategies. Thus we developed a model and found that the concavity of the reproduction-survival curve can still have a large impact on life history strategies in an ecological model with Darwinian evolution.