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In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B ′ / B = F ⊕ − F ⊖ , where F ⊖ represents a reaction factor reflecting the stress proportional to the active group's percentage variation. Conversely, F ⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F ⊕ = 0 , we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model's behavior and its implications for understanding disease transmission. [ABSTRACT FROM AUTHOR]

The presence of the golden mussel in Brazil is a matter of great concern and causes harm to the country, particularly affecting the power generation sector. Infestation control represents a challenge, and there is a need to mathematically describe the dynamics of the problem. This work proposes to analyze a mathematical model based on differential equations that relate the populations of larvae, mussels, and algae. For this model, the critical points and stationary states are determined, seeking steady-state conditions stability, through the basic reproduction rate. In addition, it presents the sensitivity analysis of the parameters involved. The paper results are relevant as they allow mathematical interpretation of the golden mussel infestation potential through the basic reproduction rate. Furthermore, the sensitivity analysis suggests how important the parameters are for this potential. For that matter, this work can provide baseline information to guide future control strategies as it provides quantification of the species involved over time as well as a condition for infestation. • Mussel-algae interaction model. • Stability analysis of stationary solutions of the model. • Basal reproduction rate for the golden mussel model. [ABSTRACT FROM AUTHOR]

In this paper, we present a review about mathematical models of population and community dynamics incorporating individual behaviour. The considered models consist in coupling a game theoretic model, going on at a fast time scale and that describes the change of tactics among individuals in a population or in a community to a model going on at a slow time scale describing the effects in the long term of individual tactics on reproduction and mortality of the populations. As application, an extension of a stage-structured population with intraindividual behavioural variability is presented. Individuals can adopt three different tactics: hawk, dove and bully. We consider a stage-structured population with immature and mature individuals. A mature individual experiences the different tactics in his life and it is assumed that the game is played at a fast time scale in comparison to population dynamics. This fast part of the model is coupled to a slow part, which describes the growth of each sub-population. By use of aggregation of variables methods, we obtain a reduced system of two differential equations governing immature and total mature sub-populations at the slow time scale. The analysis of the model shows that when the cost of fightings is smaller, the proportion of hawks is larger. The total population size equilibrium shows a maximum with respect to the gain of the game. [ABSTRACT FROM AUTHOR]

Abstract: Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mechanistic mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. The model generates successive estrous cycles of 21 days, with three waves of follicle growth per cycle. The model contains 12 differential equations and 54 parameters. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included in the model are based on relations that in the literature have only been described qualitatively (i.e. stimulation and inhibition), the output of the model is surprisingly well in line with empirical data. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences. [Copyright &y& Elsevier]

A mathematical model (SEPNS) for rumour spreading on social media is proposed here with the required differential equations. Microscopic observations are considered here to obtain the compartments in this epidemiological model. The predictions based on this model can help social media analysts provide valuable and specific suggestions in business and politics. The equilibrium points are obtained for this model. Later, the stability analysis based on basic reproduction number R 0 is done for both the rumour free equilibrium and the endemic equilibrium. Finally, numerical simulation of the model is done to understand the influence of different parameters during rumour spread. [ABSTRACT FROM AUTHOR]

We present a model for the advantage of sexual reproduction in multicellular long-lived species in a world of structured resources in short supply. The model combines features of the Tangled Bank and the Red Queen hypothesis of sexual reproduction and is of broad applicability. The model is ecologically explicit with the dynamics of resources and consumers being modelled by differential equations. The life history of consumers is shaped by body mass-dependent rates as implemented in the metabolic theory of ecology. We find that over a broad range of parameters, sexual reproduction wins despite the two-fold cost of producing males, due to the advantage of producing offspring that can exploit underutilized resources. The advantage is largest when maturation and production of offspring set in before the resources of the parents become depleted, but not too early, due to the cost of producing males. The model thus leads to the dominance of sexual reproduction in multicellular animals living in complex environments, with resource availability being the most important factor affecting survival and reproduction. [ABSTRACT FROM AUTHOR]

We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f (S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number. [ABSTRACT FROM AUTHOR]