A generalized Gompertz growth model with applications and related birth-death processes

Tumor growth and population modeling in a toxicant-stressed random environment

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

Microbial Growth under Limiting Conditions-Future Perspectives

Microorganisms rule the functioning of our planet and each one of the individual macroscopic living creature. Nevertheless, microbial activity and growth status have always been challenging tasks to determine both in situ and in vivo. Microbial activity is generally related to growth, and the growth rate is a result of the availability of nutrients under adequate or adverse conditions faced by microbial cells in a changing environment. Most studies on microorganisms have been carried out under optimum or near-optimum growth conditions, but scarce information is available about microorganisms at slow-growing states (i.e., near-zero growth and maintenance metabolism). This study aims to better understand microorganisms under growth-limiting conditions. This is expected to provide new perspectives on the functions and relevance of the microbial world. This is because (i) microorganisms in nature frequently face conditions of severe growth limitation, (ii) microorganisms activate singular pathways (mostly genes remaining to be functionally annotated), resulting in a broad range of secondary metabolites, and (iii) the response of microorganisms to slow-growth conditions remains to be understood, including persistence strategies, gene expression, and cell differentiation both within clonal populations and due to the complexity of the environment.

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary.

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.