Mathematical medicine and biology : a journal of the IMA最新文献

Drug resistance is a significant obstacle to effective cancer treatment. To gain insights into how drug resistance develops, we adopted a concept called fitness landscape and employed a phenotype-structured population model by fitting to a set of experimental data on a drug used for ovarian cancer, olaparib. Our modeling approach allowed us to understand how a drug affects the fitness landscape and track the evolution of a population of cancer cells structured with a spectrum of drug resistance. We also incorporated pharmacokinetic (PK) modeling to identify the optimal dosages of the drug that could lead to long-term tumor reduction. We derived a formula that indicates that maximizing variation in plasma drug concentration over a dosing interval could be important in reducing drug resistance. Our findings suggest that it may be possible to achieve better treatment outcomes with a drug dose lower than the levels recommended by the drug label. Acknowledging the current limitations of our work, we believe that our approach, which combines modeling of both PK and drug resistance evolution, could contribute to a new direction for better designing drug treatment regimens to improve cancer treatment.

Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction-diffusion model of the climate-vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture.

The emergence of multiple strains of SARS-COV-2 has made it complicated to predict and control the COVID-19 pandemic. Although some vaccines have been effective in reducing the severity of the disease, these vaccines are designed for a specific strain of the virus and are usually less effective for other strains. In addition, the waning of vaccine-induced immunity, reinfection of recovered people, and incomplete vaccination are challenging to the vaccination program. In this study, we developed a detailed model to describe the multi-strain transmission dynamics of COVID-19 under vaccination. We implemented our model to examine the impact of inter-strain transmission competition under vaccination on the critical outbreak indicators: hospitalized cases, undiagnosed cases, basic reproduction numbers, and the overtake-time by a new strain to the existing strain. In particular, our results on the dependence of the overtake-time on vaccination rates, progression-to-infectious rate, and relative transmission rates provide helpful information for managing a pandemic with circulating two strains. Furthermore, our results suggest that a reduction in the relative transmission rates and a decrease in vaccination dropout rates or an increase in vaccination rates help keep the reproduction number of both strains below unity and keep the number of hospitalized cases and undiagnosed cases at their lowest levels. Moreover, our analysis shows that the second and booster-dose vaccinations are useful for further reducing the reproduction number.

Structure-function relationships occur throughout the sciences. Motivated by optimization of such systems, we develop a framework for estimating the input modes from the singular value decomposition from the action of the forward operator alone. These can then be used to determine the input (structure) changes, which induce the largest output (function) changes. The accuracy of the estimate is determined by reference to the method of snapshots. The proposed method is demonstrated on several example problems, and finally used to approximate the optimal airway treatment set for a problem in respiratory physiology.

We employ the multiphase, moving boundary model of Byrne et al. (2003, Appl. Math. Lett., 16, 567-573) that describes the evolution of a motile, viscous tumour cell phase and an inviscid extracellular liquid phase. This model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tumour edge, and here we characterize and analyse its travelling-wave and pattern-forming behaviour. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tumour growth or extinction, respectively. A travelling-wave analysis allows us to find the corresponding wave speed, as well as criteria for the growth or extinction of the tumour. Furthermore, a stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. Finally, we discuss how the initial cell distribution, as well as parameters related to cellular motion and cell-liquid drag, control the qualitative features of patterned solutions.

The Fisher-Kolmogorov-Petrovsky-Piskunov (KPP) model, and generalizations thereof, involves simple reaction-diffusion equations for biological invasion that assume individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate $lambda $. For the Fisher-KPP model, biologically relevant initial conditions lead to long-time travelling wave solutions that move with speed $c=2sqrt {lambda D}$. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically relevant initial conditions lead to travelling waves that move with speed $c=2sqrt {lambda D}> 0$. This means that, for biologically relevant initial data, the Fisher-KPP model cannot be used to study invasion with $c ne 2sqrt {lambda D}$, or retreating travelling waves with $c < 0$. Here, we reformulate the Fisher-KPP model as a moving boundary problem and show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front that can propagate with any wave speed, $-infty < c < infty $. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub.