Bulletin of Mathematical Biology最新文献

Mosquitoes are important vectors for the transmission of some major infectious diseases of humans, i.e., malaria, dengue, West Nile Virus and Zika virus. The burden of these diseases is different for different regions, being highest in tropical and subtropical areas, which have high annual rainfall, warm temperatures, and less pronounced seasonality. The life cycle of mosquitoes consists of four distinct stages: eggs, larvae, pupae, and adults. These life stages have different mortality rates and only adults can reproduce. Seasonal weather may affect the population dynamics of mosquitoes, and the relative abundance of different mosquito stages. We developed a stage-structured model that considers laboratory experiments describing how temperature and rainfall affects the reproduction, maturation and survival of different Anopheles mosquito stages, the species that transmits the parasite that causes malaria. We consider seasonal temperature and rainfall patterns and describe the stage-structured population dynamics of the Anopheles mosquito in Ain Mahbel, Algeria, Cape Town, South Africa, Nairobi, Kenya and Kumasi, Ghana. We find that neglecting seasonality leads to significant overestimation or underestimation of mosquito abundance. We find that depending on the region, mosquito abundance: peaks one, two or four times a year, periods of low abundance are predicted to occur for durations ranging from six months (Ain Mahbel) to not at all (Nairobi); and seasonal patterns of relative abundance of stages are substantially different. The region with warmer temperatures and higher rainfall across the year, Kumasi, Ghana, is predicted to have higher mosquito abundance, which is broadly consistent with reported malaria deaths relative to the other countries considered by our study. Our analysis reveals distinct patterns in mosquito abundance across different months and regions. Control strategies often target one specific life stage, for example, applying larvicides to kill mosquito larvae, or spraying insecticides to kill adult mosquitoes. Our findings suggest that differences in seasonal weather affect mosquito stage structure, and that the best approaches to vector control may differ between regions in timing, duration, and efficacy.

We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models of flat epithelia to investigate the influence of curvature for mechanical relaxation. We represent the mechanics of a cell body either by straight springs, or by curved springs that follow the curve's shape. To understand the collective dynamics of the cells, we devise an appropriate continuum limit in which the number of cells and the length of the substrate are constant but the number of springs tends to infinity. In this limit, cell density is governed by a diffusion equation in arc length coordinates, where diffusion may be linear or nonlinear depending on the choice of the spring restoring force law. Our results have important implications about modelling cells on curved geometries: (i) curved and straight springs can lead to different dynamics when there is a finite number of springs, but they both converge quadratically to the dynamics governed by the diffusion equation; (ii) in the continuum limit, the curvature of the tissue does not affect the mechanical relaxation of cells within the layer nor their tangential stress; (iii) a cell's normal stress depends on curvature due to surface tension induced by the tangential forces. Normal stress enables cells to sense substrate curvature at length scales much larger than their cell body, and could induce curvature dependences in experiments.

Hereditary diffuse gastric cancer is characterized by an increased risk of diffuse gastric cancer and lobular breast cancer, and is caused by pathogenic germline variants of E-cadherin and $\alpha$ -E-catenin, which are key regulators of cell-cell adhesion. However, how the loss of cell-cell adhesion promotes cell dissemination remains to be fully understood. Therefore, a three-dimensional computer model was developed to describe the initial steps of diffuse gastric cancer development. In this model, we have implemented a cellular Potts approach that contemplates cell adhesion to other cells and to the extracellular matrix, cell extrusion from the gastric epithelia, and subsequent proliferation. We demonstrate that early disease features are determined by decreased adhesion of mutant cells to their normal epithelial neighbors, with concomitant increased attachment to matrix components. Importantly, our simulation shows how mechanical pressure and uncontrolled proliferation of mutant cells lead to modifications in cell shape and in gastric gland morphology. In conclusion, this work underscores the potential of computational models to elucidate the role of cellular and noncellular components in gastric cancer that may be relevant targets in therapeutic interventions.

We investigate the impact of differential vaccine effectiveness, waning immunity, and natural cross-immunity on the capacity for vaccine-induced strain replacement in two-strain models of infectious disease spread. We focus specifically on the case where the first strain is more transmissible but the second strain is more immune-resistant. We consider two cases on vaccine-induced immunity: (1) a monovalent model where the second strain has immune escape with respect to vaccination; and (2) a bivalent model where the vaccine remains equally effective against both strains. Our analysis reaffirms the capacity for vaccine-induced strain replacement under a variety of circumstances; surprisingly, however, we find that which strain is preferred depends sensitively on the degree of differential vaccine effectiveness. In general, the monovalent model favors the more immune-resistant strain at high vaccination levels while the bivalent model favors the more transmissible strain at high vaccination levels. To further investigate this phenomenon, we parametrize the bifurcation space between the monovalent and bivalent model.

In this work we analytically investigate the alignment mechanism of self-propelled ellipse-shaped cells in two spatial dimensions interacting via overlap avoidance. By considering a two-cell system and imposing certain symmetries, we obtain an analytically tractable dynamical system, which we mathematically analyse in detail. We find that for elongated cells there is a half-stable steady state corresponding to perfect alignment between the cells. Whether cells move towards this state (i.e., become perfectly aligned) or not is determined by where in state space the initial condition lies. We find that a separatrix splits the state space into two regions, which characterise these two different outcomes. We find that some self-propulsion is necessary to achieve perfect alignment, however too much self-propulsion hinders alignment. Analysing the effect of small amounts of self-propulsion offers an insight into the timescales at play when a trajectory is moving towards the point of perfect alignment. We find that the two cells initially move apart to avoid overlap over a fast timescale, and then the presence of self-propulsion causes them to move towards a configuration of perfect alignment over a much slower timescale. Overall, our analysis highlights how the interaction between self-propulsion and overlap avoidance is sufficient to generate alignment.

Spatial distributions of morphogens provide positional information in developing systems, but how the distributions are established and maintained remains an open problem. Transport by diffusion has been the traditional mechanism, but recent experimental work has shown that cells can also communicate by filopodia-like structures called cytonemes that make direct cell-to-cell contacts. Here we investigate the roles each may play individually in a complex tissue and how they can jointly establish a reliable spatial distribution of a morphogen. To this end, we formulate models that capture fundamental aspects of various cytoneme-based transport mechanisms. In simple cases, exact solutions are attainable, and in more complex cases, we discuss results of numerical simulations.

The human immune system can recognize, attack, and eliminate cancer cells, but cancers can escape this immune surveillance. Variants of ecological predator-prey models can capture the dynamics of such cancer control mechanisms by adaptive immune system cells. These dynamical systems describe, e.g., tumor cell-effector T cell conjugation, immune cell activation, cancer cell killing, and T cell exhaustion. Target (tumor) cell-T cell conjugation is integral to the adaptive immune system's cancer control and immunotherapy. However, whether conjugate dynamics should be explicitly included in mathematical models of cancer-immune interactions is incompletely understood. Here, we analyze the dynamics of a cancer-effector T cell system and focus on the impact of explicitly modeling the conjugate compartment to investigate the role of cellular conjugate dynamics. We formulate a deterministic modeling framework to compare possible equilibria and their stability, such as tumor extinction, tumor-immune coexistence (tumor control), or tumor escape. We also formulate the stochastic analog of this system to analyze the impact of demographic fluctuations that arise when cell populations are small. We find that explicit consideration of a conjugate compartment can (i) change long-term steady-state, (ii) critically change the time to reach an equilibrium, (iii) alter the probability of tumor escape, and (iv) lead to very different extinction time distributions. Thus, we demonstrate the importance of the conjugate compartment in defining tumor-effector T cell interactions. Accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression.

The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or lateral gene transfer events between lineages, and so the history of life is more accurately described by a rooted phylogenetic network. Nevertheless, phylogenetic networks may be complex and difficult to interpret, so biologists sometimes prefer a tree that summarises the central tree-like trend of evolution. In this paper, we formally investigate methods for transforming an arbitrary phylogenetic network into a tree (on the same set of leaves) and ask which ones (if any) satisfy a simple consistency condition. This consistency condition states that if we add additional species into a phylogenetic network (without otherwise changing this original network) then transforming this enlarged network into a rooted phylogenetic tree induces the same tree on the original set of species as transforming the original network. We show that the LSA (lowest stable ancestor) tree method satisfies this consistency property, whereas several other commonly used methods (and a new one we introduce) do not. We also briefly consider transformations that convert arbitrary phylogenetic networks to another simpler class, namely normal networks.

Linear compartmental models are often employed to capture the change in cell type composition of cancer cell populations. Yet, these populations usually grow in a nonlinear fashion. This begs the question of how linear compartmental models can successfully describe the dynamics of cell types. Here, we propose a general modeling framework with a nonlinear part capturing growth dynamics and a linear part capturing cell type transitions. We prove that dynamics in this general model are asymptotically equivalent to those governed only by its linear part under a wide range of assumptions for nonlinear growth.

One of the strategies used in some countries to contain the COVID-19 epidemic has been the test-and-isolate policy, generally coupled with contact tracing. Such strategies have been examined in several simulation models, but a theoretical analysis of their effectiveness in simple epidemic model is, to our knowledge, missing. In this paper, we present four epidemic models of either SIR or SEIR type, in which it is assumed that at fixed times the whole population (or a part of the population) is tested and, if positive, isolated. We find the conditions for an epidemic to go extinct under such a strategy; for these types of models we provide an appropriate definition of $R_0$ , that can be computed either analytically or numerically. Finally, we show numerically that the final-size relation of SIR models approximately holds for the four models, over a large parameter range.