Journal of Mathematical Biology最新文献

In this paper, we propose and analyze a nonautonomous model that describes the dynamics of a size-structured consumer interacting with an unstructured resource. We prove the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We derive conditions on the model parameters that result in persistence and extinction of the population via the upper-lower solution technique. We verify and complement the theoretical results through numerical simulations.

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model's qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

To maintain renewing epithelial tissues in a healthy, homeostatic state, cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic regulation often rely on crowding feedback control: cells are able to sense the cell density in their environment, via various molecular and mechanosensing pathways, and respond by adjusting division, differentiation, and cell state transitions appropriately. Here, we determine, via a mathematically rigorous framework, which general conditions for the crowding feedback regulation (i) must be minimally met, and (ii) are sufficient, to allow the maintenance of homeostasis in renewing tissues. We show that those conditions naturally allow for a degree of robustness toward disruption of regulation. Furthermore, intrinsic to this feedback regulation is that stem cell identity is established collectively by the cell population, not by individual cells, which implies the possibility of 'quasi-dedifferentiation', in which cells committed to differentiation may reacquire stem cell properties upon depletion of the stem cell pool. These findings can guide future experimental campaigns to identify specific crowding feedback mechanisms.

Emerging and re-emerging pathogens are latent threats in our society with the risk of killing millions of people worldwide, without forgetting the severe economic and educational backlogs. From COVID-19, we learned that self isolation and quarantine restrictions (confinement) were the main way of protection till availability of vaccines. However, abrupt lifting of social confinement would result in new waves of new infection cases and high death tolls. Here, inspired by how an extracellular solution can make water move into or out of a cell through osmosis, we define confinement tonicity. This can serve as a standalone measurement for the net direction and magnitude of flows between the confined and deconfined susceptible compartments. Numerical results offer insights on the effects of easing quarantine restrictions.

COVID-19 is a respiratory disease triggered by an RNA virus inclined to mutations. Since December 2020, variants of COVID-19 (especially Delta and Omicron) continuously appeared with different characteristics that influenced death and transmissibility emerged around the world. To address the novel dynamics of the disease, we propose and analyze a dynamical model of two strains, namely native and mutant, transmission dynamics with mutation and imperfect vaccination. It is also assumed that the recuperated individuals from the native strain can be infected with mutant strain through the direct contact with individual or contaminated surfaces or aerosols. We compute the basic reproduction number, $R_0$ , which is the maximum of the basic reproduction numbers of native and mutant strains. We prove the nonexistence of backward bifurcation using the center manifold theory, and global stability of disease-free equilibrium when $R_0<1$ , that is, vaccine is effective enough to eliminate the native and mutant strains even if it cannot provide full protection. Hopf bifurcation appears when the endemic equilibrium loses its stability. An intermediate mutation rate ${\nu }_1$ leads to oscillations. When ${\nu }_1$ increases over a threshold, the system regains its stability and exhibits an interesting dynamics called endemic bubble. An analytical expression for vaccine-induced herd immunity is derived. The epidemiological implication of the herd immunity threshold is that the disease may effectively be eradicated if the minimum herd immunity threshold is attained in the community. Furthermore, the model is parameterized using the Indian data of the cumulative number of confirmed cases and deaths of COVID-19 from March 1 to September 27 in 2021, using MCMC method. The cumulative cases and deaths can be reduced by increasing the vaccine efficacies to both native and mutant strains. We observe that by considering the vaccine efficacy against native strain as 90%, both cumulative cases and deaths would be reduced by 0.40%. It is concluded that increasing immunity against mutant strain is more influential than the vaccine efficacy against it in controlling the total cases. Our study demonstrates that the COVID-19 pandemic may be worse due to the occurrence of oscillations for certain mutation rates (i.e., outbreaks will occur repeatedly) but better due to stability at a lower infection level with a larger mutation rate. We perform sensitivity analysis using the Latin Hypercube Sampling methodology and partial rank correlation coefficients to illustrate the impact of parameters on the basic reproduction number, the number of cumulative cases and deaths, which ultimately sheds light on disease mitigation.

We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton–Watson branching process and then its size follows an almost deterministic path until reaching its maximum, sustainable by the habitat. In this paper we put forward an alternative and, in fact, more accurate approximation which suggests that the population size behaves as a special nonlinear transformation of the Galton–Watson process from the very beginning.

We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a standing assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. We then define the basic reproduction number of viral infection $R_0$ and prove (by the uniform persistence theory, Lyapunov function technique and LaSalle invariance principle) that the infection-free steady state $E_0$ is globally asymptotically stable if $R_0<1$ . When $R_0>1$ , then $E_0$ becomes unstable, and another basic reproduction number of CTL response $R_1$ becomes the dynamic threshold in the sense that if $R_1<1$ , then the CTL-inactivated steady state $E_1$ is globally asymptotically stable; and if $R_1>1$ , then the immune response is uniform persistent and, under an additional technical condition the CTL-activated steady state $E_2$ is globally asymptotically stable. To establish the global stability results, we need to prove point dissipativity, obtain uniform persistence, construct suitable Lyapunov functions, and apply the LaSalle invariance principle.

Phylogenetic diversity is a popular measure for quantifying the biodiversity of a collection Y of species, while phylogenetic diversity indices provide a way to apportion phylogenetic diversity to individual species. Typically, for some specific diversity index, the phylogenetic diversity of Y is not equal to the sum of the diversity indices of the species in Y. In this paper, we investigate the extent of this difference for two commonly-used indices: Fair Proportion and Equal Splits. In particular, we determine the maximum value of this difference under various instances including when the associated rooted phylogenetic tree is allowed to vary across all rooted phylogenetic trees with the same leaf set and whose edge lengths are constrained by either their total sum or their maximum value.

Clinical and pre-clinical data suggest that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.

In the Antarctic, the whale population had been reduced dramatically due to the unregulated whaling. It was expected that Antarctic krill, the main prey of whales, would grow significantly as a consequence and exploratory krill fishing was practiced in some areas. However, it was found that there has been a substantial decline in abundance of krill since the end of whaling, which is the phenomenon of krill paradox. In this paper, to study the krill-whale interaction we revisit a harvested predator-prey model with Holling I functional response. We find that the model admits at most two positive equilibria. When the two positive equilibria are located in the region $\{(N,P)|0\le N<2N_c,P\ge 0\}$ , the model exhibits degenerate Bogdanov-Takens bifurcation with codimension up to 3 and Hopf bifurcation with codimension up to 2 by rigorous bifurcation analysis. When the two positive equilibria are located in the region $\{(N,P)|N>2N_c,P\ge 0\}$ , the model has no complex bifurcation phenomenon. When there is one positive equilibrium on each side of $N=2N_c$ , the model undergoes Hopf bifurcation with codimension up to 2. Moreover, numerical simulation reveals that the model not only can exhibit the krill paradox phenomenon but also has three limit cycles, with the outmost one crosses the line $N=2N_c$ under some specific parameter conditions.