Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19

Abstract

In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differential equations. Moreover, the method of piecewise arguments is used to discretize the continuous system. The mathematical system is said to reveal six equilibria, namely, extinction equilibrium, boundary equilibrium, quarantined-free equilibrium, exposure-free equilibrium, endemic equilibrium, and the equilibrium free from susceptible population. Local stability conditions are developed for our discrete-time mathematical system about each of its equilibrium point. The existence of period-doubling bifurcation and chaos is studied in the absence of isolated population. It is shown that our system will become unstable and experiences the chaos when the quarantined compartment is empty, which is true in biological meanings. The existence of Neimark–Sacker bifurcation is studied for the endemic equilibrium point. Moreover, it is shown numerically that our discrete-time mathematical system experiences the period-doubling bifurcation about its endemic equilibrium. To control the period-doubling bifurcation, Neimark–Sacker bifurcation, a generalized hybrid control methodology is used. Moreover, this model is analyzed along with generalized hybrid control in order to eliminate chaos and oscillation epidemiologically presenting the significance of quarantine in the COVID-19 environment.

Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination

“…The fractional derivative can be regarded as the globalization of the integral derivative, which can show more properties that the integral derivative does not have. Many scholars have applied fractional derivative differential equations to study the spread of COVID-19, and many important research results have been obtained [31] , [32] , [33] , [34] , [35] , [36] . If we consider fractional COVID-19 model for parameter estimation, different results with higher fitting degree may be obtained, and the measures taken may be changed.…”

“…One of the important ideas is to study the spread of COVID-19 through mathematical models. To that end, a number of mathematical models have been developed over the past two years to study local infections, estimate peaks in the number of people infected, and suggest ways to control the spread of the disease [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] .…”

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

“…Here, we discuss the Neimark–Sacker bifurcation experienced by system ( 5 ) about under certain mathematical conditions. For further study of bifurcation theory and to better understand this surprising behaviuor of discrete-time mathematical systems, we refer readers to [ 42 , 43 , 44 , 45 , 46 , 47 , 48 ]. Here, we use the standard theory of bifurcation for study of the Neimark–Sacker bifurcation of system ( 5 ) at .…”

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

“…Numerous mathematical studies have investigated the dynamics of SARS-CoV-2 and its co-infection with other diseases such as dengue [18] , HIV [19] , diabetes [20] , [21] , [22] , [23] , tuberculosis [24] , [25] and malaria [26] , [27] , [28] . Most of the co-infection models in the literature do not include the assumption that susceptible individuals can get incident co-infection with the two diseases (an assumption which is possible for some diseases, and yet always ignored).…”