Dynamics of an epidemic system with prey herd behavior and alternative resource to predator

Abstract

A heterogeneous predator–prey system with herd behavior of prey is proposed. The predator individuals are affected by a disease. The predator is provided with alternative resources for long time survival. The objective of this study is to study the role of the alternative resource for controlling disease in a heterogeneous system. The dynamical behavior of the system is investigated throughout the theoretical studies and the results are verified using numerical simulations. The system is locally, as well as globally, stable under certain conditions. Also, the system undergoes Hopf bifurcation at a critical level of infection. The obtained results show that a disease-free system can be achieved by supplying a suitable alternative resource. The present study in an epidemic system introduces a new platform for controlling disease.

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

“…There are several variants [2][3][4][5][6][7][8][9][10] of the SIR model, including stochastic variants [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and there is a large amount of related work in the context of the SIR model in the presence of vaccination. Many works deal with vaccination strategies [13,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], transmission among an interconnected group or population [44] and vaccination behavior by coupling the epidemic spreading with human decisions [45], or policies [46,47] using the SIR model with limited resources [48].…”

Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

“…Using the identities 2(1 + e −2Y ) −1 = 1 + tanh Y and 2(1 − e −2Y ) −1 = 1 + coth Y we combine the results (C6) and (C11) to the analytical approximation of the SIR-model equations at all reduced times, stated in Eqs. (10), (11), and (12). A comparison with the exact numerical solution of the SIR model is provide in Fig.…”

“…The SIR system is the simplest and most fundamental of the compartmental models and its variations. [3][4][5][6][7][8][9][10][11][12][13][14][15] The considered population of N 1 persons is assigned to the three compartments s (susceptible), i (infectious), or r (recovered/removed). Persons from the population may progress with time between these compartments with given infection (a(t)) and recovery rates (µ(t)) which in general vary with time due to non-pharmaceutical interventions taken during the pandemic evolution.…”

Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions

“…The Susceptible-Infectious-Recovered (SIR) model has been developed nearly hundred years ago [1,2] to understand the time evolution of infectious diseases in human populations. The SIR system is the simplest and most fundamental of the compartmental models and its variations [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The considered population of N ≫ 1 persons is assigned to the three compartments s (susceptible), i (infectious), or r (recovered/removed).…”