Range Shifts Under Constant-Speed and Accelerated Climate Warming

Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching

Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that many established in vivo measurements of protein dynamics average out the spatial dimensions. Here, we are motivated by recent experiments on the binding dynamics of the RNA-binding protein PTBP3 in RNP granules of frog oocytes based on fluorescence recovery after photobleaching (FRAP) measurements. FRAP is a widely-used experimental technique for probing protein dynamics in living cells, and is often modeled using simple reaction-diffusion models of the protein dynamics. We show that current methods of structural and practical parameter identifiability provide limited insights into identifiability of kinetic parameters for these PDE models and spatially-averaged FRAP data. We thus propose a pipeline for assessing parameter identifiability and for learning parameter combinations based on re-parametrization and profile likelihoods analysis. We show that this method is able to recover parameter combinations for synthetic FRAP datasets and investigate its application to real experimental data.

Recursive Zero-COVID model and quantitation of control efforts of the Omicron epidemic in Jilin province

Since the beginning of March 2022, the epidemic due to the Omicron variant has developed rapidly in Jilin Province. To figure out the key controlling factors and validate the model to show the success of the Zero-COVID policy in the province, we constructed a Recursive Zero-COVID Model quantifying the strength of the control measures, and defined the control reproduction number as an index for describing the intensity of interventions. Parameter estimation and sensitivity analysis were employed to estimate and validate the impact of changes in the strength of different measures on the intensity of public health preventions qualitatively and quantitatively. The recursive Zero-COVID model predicted that the dates of elimination of cases at the community level of Changchun and Jilin Cities to be on April 8 and April 17, respectively, which are consistent with the real situation. Our results showed that the strict implementation of control measures and adherence of the public are crucial for controlling the epidemic. It is also essential to strengthen the control intensity even at the final stage to avoid the rebound of the epidemic. In addition, the control reproduction number we defined in the paper is a novel index to measure the intensity of the prevention and control measures of public health.

ROLE OF ALLEE EFFECT AND HARVESTING OF A FOOD-WEB SYSTEM IN THE PRESENCE OF SCAVENGERS

The role of scavengers, which consume the carcasses of predators along with predation of the prey, has been ignored in comparisons to herbivores and predators. It has now become a topic of high interest among researchers working with food-web systems of prey–predator interactions. The food-web considered in these works contains prey, predators, and scavengers as the third species. In this work, we attempt to study a food-web model of these species in the presence of the multiplicative Allee effect and harvesting. It is observed that this makes the model more complex in the form of multiple co-existing steady states. The conditions for the existence and local stability of all possible steady states of the proposed system are analyzed. The global stability of the steady state lying on the x-axis and the interior steady state have been discussed by choosing suitable Lyapunov functions. The existence conditions for saddle-node and Hopf bifurcations are derived analytically. The stability of Hopf bifurcating periodic solutions with respect to both Allee and harvesting constants is examined. It is also observed that multiple Hopf bifurcation thresholds occur for harvesting parameters in the case of two co-existing steady states, which indicates that the system may regain its stability. The proposed model is also studied beyond Hopf bifurcation thresholds, where we have observed that the model is capable of exhibiting period-doubling routes to chaos, which can be controlled by a suitable choice of Allee and harvesting parameters. The largest Lyapunov exponents and sensitivity to initial conditions are examined to ensure the chaotic nature of the system.

Analysis of a COVID-19 Epidemic Model with Seasonality

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.