Journal of Mathematical Biology最新文献

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that forecast wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model's starting parameters and peak incidence as a system of two equations that can be solved computationally. We demonstrate how to calculate SIR parameter estimates - which describe disease dynamics such as transmission and recovery rates - using this method, and determine that there is a noticeable loss in accuracy whenever prevalence data is misspecified as incidence data. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation.

The Sterile Insect Technique (SIT) is a biological control method used to reduce or eliminate pest populations or disease vectors. This technique involves releasing sterilized insects that, upon mating with the wild population, produce no offspring, leading to a decline or eventual eradication of the target species. We incorporate a spatial dimension by modeling the pest/vector population as being distributed across multiple patches, with both wild and released sterile insects migrating between these patches at predetermined rates. We mainly focus on a two-patch system. This study has two primary objectives: first, to derive sufficient conditions for achieving the elimination of the wild population through SIT, whether releases occur in one patch or in both patches. In particular, we provide an estimate of the minimal release rates to reach elimination thanks to the diffusion rates between patches. This is the first time that such a result is given in a general manner. Second, we study an optimal SIT control strategy, where we minimize the total amount of sterile insects to release, and show that, within one patch, it can successfully reduce the wild population in that patch to a desired level within a finite time frame, provided that the migration rates between patches are sufficiently low. Numerical simulations are employed to illustrate these results and further analyze the outcomes.

We consider a reaction-diffusion model with free boundaries in one space dimension for a single population species with density u(t, x) and population range [g(t), h(t)]. The equations governing the evolution of the range boundary are deduced from the biological assumption that the species maintains its population density at a fixed positive level at the range boundary by advancing or retreating the fronts. Our mathematical results suggest that the Allee effects are eliminated if the species maintains its population density at suitable levels at the range boundary, namely with such a strategy at the range edge the species can invade the environment successfully with all admissible initial populations, exhibiting the dynamics of super invaders. Numerical simulations are used to help understand what happens if the population density levels at the range boundary are maintained in other ranges.

During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within and between cells. Here, we develop and present a model-independent ordinary differential equation (ODE) framework for analyzing pattern formation in a homogeneous cell array. In contrast to traditional approaches that focus on specific equations, our method relies solely on general assumptions about global intercellular communication (between cells) and qualitative properties of local intracellular biochemical signaling (within cells). Prior work has shown that global intercellular communication networks alone determine the possible emergent patterns in a generic system. We build on these results by demonstrating that additional constraints on the local intracellular signaling network lead to a single stable pattern which depends on the qualitative features of the network. Our framework enables the prediction of cell fate patterns with minimal modeling assumptions, and provides a powerful tool for inferring unknown interactions within signaling networks by analyzing tissue-level patterns.

Fire blight is a bacterial plant disease that affects apple and pear trees. We present a mathematical model for its spread in an orchard during bloom. This is a PDE-ODE coupled system, consisting of two semilinear PDEs for the pathogen, coupled to a system of three ODEs for the stationary hosts. Exploratory numerical simulations suggest the existence of travelling waves, which we subsequently prove, under some conditions on parameters, using the method of upper and lower bounds and Schauder's fixed point theorem. Our results are likely not optimal in the sense that our constraints on parameters, which can be interpreted biologically, are sufficient for the existence of travelling waves, but probably not necessary. Possible implications for fire blight biology and management are discussed.

We consider stochastic population processes that are almost surely absorbed at the origin within finite time. Our interest is in the quasistationary distribution,  $u$ , and the expected time, $\tau$ , from quasistationarity to extinction, both of which we study via WKB approximation. This approach involves solving a Hamilton-Jacobi partial differential equation specific to the model. We provide conditions under which analytical solution of the Hamilton-Jacobi equation is possible, and give the solution. This provides a first approximation to both  $u$ and  $\tau$ . We provide further conditions under which a corresponding 'transport equation' may be solved, leading to an improved approximation of  $u$ . For multitype birth and death processes, we then consider an alternative approximation for  $u$ that is valid close to the origin, provide conditions under which the elements of this alternative approximation may be found explicitly, and hence derive an improved approximation for  $\tau$ . We illustrate our results in a number of applications.

When an exotic species is introduced outside its natural range, new interspecific interactions with native species may arise. These interactions can induce phenotypic changes, which may originate from phenotypic plasticity or adaptive processes. Phenotypic change may play an important role in biological invasions, either by promoting or by preventing its success. In this work, a mathematical modeling approach is used to study a native predator-prey system exposed to an exotic species that predates on the native species and that also competes by interference with the native predator. This proposed approach allows to describe the eco-evolutionary dynamics involving the inducible defense of the prey and the inducible offense of both predators. The model is represented by a system of ordinary differential equations (ODEs), analyzed using advanced analytical and numerical methods. Specifically, we applied the qualitative theory of ODEs and developed numerical algorithms for parameter sweeps. Parameter values for the numerical experiments were based on the American mink, one of the most harmful invasive species in Europe and South America. The results show that the role of phenotypic change in invasion success depends on three components: the efficiency of the new trait values, the associated costs, and the speed of trait change. The specific conditions that lead to an unsuccessful invasion are: the prey's defense efficiency against the exotic predator is higher than its defense efficiency against the native predator. The cost imposed by the exotic predator is greater than the cost imposed by the native predator. Lastly, the speed of phenotypic change is faster in the native predator than in the exotic predator.

An unconventional and environmentally friendly mosquito management approach offers a sustainable solution that protects both the environment and human health. One such method is the Sterile Insect Technique (SIT), which holds promise as a mosquito control strategy by releasing sterilized male mosquitoes into the wild-type (WT) mosquito population. Since the success of SIT depends on the strategic planning of sterile mosquito releases, this paper examines a stage-structured model for mosquito populations with a density-dependent threshold for sterile male mosquito release, where releases occur only when the ratio of WT to sterile mosquito populations exceeds a critical threshold. Using intermittent releases, the proposed SIT model is designed to optimally align the release of sterile male mosquitoes with WT and sterile mosquito population densities, maintaining WT mosquito suppression at a predefined threshold and offering a more effective alternative to continuous release strategies. We employ Filippov's modelling approach to investigate how intermittent releases, represented by piecewise-smooth functions, affect the dynamics of the system, particularly when mosquito populations exceed the predefined threshold. To explore the dynamical complexities, we employ Filippov's convex method by defining the vector field in the discontinuous region as convex combinations of adjacent fields, allowing for the analysis of sliding motion and the identification of discontinuity-induced bifurcations through differential inclusions. Our findings identify the minimum release rate of sterile mosquitoes required to achieve the desired suppression level, highlighting the need to increase this rate due to increased WT mosquito immigration, reduced survival and mating fitness of sterile mosquitoes, and limitations in mosquito surveillance accuracy.

The time-elapsed model for neural assemblies is a nonlinear age-structured equation where the renewal term describes the network activity and influences the discharge rate, possibly with a delay due to the length of connections. We first solve a long standing question, namely that an inhibitory network without delay can promote desynchronization and stabilizes network activity by proving rigorously that the solution converges to a unique steady state. Our approach is based on the observation that a non-expansion property holds. However a non-degeneracy condition is needed and, besides the standard one, we introduce a new condition based on strict nonlinearity. When a delay is included, following previous works for Fokker-Planck models, we prove that the network can generate periodic solutions, both in inhibitory and excitatory networks. To this end, we introduce a new formalism to establish rigorously this property for large delays. Moreover, the fundamental contraction property can extend to other age-structured equations and systems.

This paper presents an extended mathematical model for tumor angiogenesis incorporating oxygen dynamics as a main regulator. We enhance a five-component PDE system describing endothelial cells, proteases, inhibitors, extracellular matrix, and oxygen concentration, with a focus on their spatiotemporal interactions. We establish existence, uniqueness, and boundedness of solutions through a mathematical analysis. A numerical scheme using method of lines and fourth-order Runge-Kutta methods is developed, with proven stability constraints and convergence properties. Numerical experiments demonstrate biologically plausible vascular formation with oxygen-mediated regulation.