Analysis of a model for waterborne diseases with Allee effect on bacteria

Abstract

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown.

Oscillation thresholds via the novel MBR method with application to oncolytic virotherapy

“…It states that in a n-dimensional dynamical system a simple Hopf bifurcation occurs at a given point if, and only if, the (n − 1)th Hurwitz determinant passes through zero, all the other ones being positive. These classical criteria have been largely used in literature, including contributions in epidemiology (e.g., macrophages-tuberculosis interaction [33], waterborne diseases [1], etc. ), crop production [20], and economics [5,18,27].…”

A Fractional-in-Time Prey–Predator Model with Hunting Cooperation: Qualitative Analysis, Stability and Numerical Approximations

“…The authors considered, in previous studies, some interacting population models that explored the mentioned characteristics (limited resources, nonlinear growth, fear effect, cooperative behavior), also in the presence of spatial dishomogeneity [13][14][15][16][17]. In the above-mentioned research, systems of both ordinary and partial differential equations have been studied.…”

“…In the above-mentioned research, systems of both ordinary and partial differential equations have been studied. Precisely, ODE descriptions for the dynamics of an intraguild predator-prey model [13] and for the spreading of waterborne diseases [15,17] have been considered and the stability of the model solutions discussed. Furthermore, in order to highlight how the spatial diffusion can both play an important role in the population evolution and lead to the formation of spatial patterns, a reaction-diffusion system modeling hunting cooperation [14] and a predator-prey system with fear and group defense [16] have been analyzed.…”