FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19

Abstract

The spread of epidemics and diseases is known to exhibit chaotic dynamics; a fact confirmed by many developed mathematical models. However, to the best of our knowledge, no attempt to realize any of these chaotic models in analog or digital electronic form has been reported in the literature. In this work, we report on the efficient FPGA implementations of three different virus spreading models and one disease progress model. In particular, the Ebola, Influenza, and COVID-19 virus spreading models in addition to a Cancer disease progress model are first numerically analyzed for parameter sensitivity via bifurcation diagrams. Subsequently and despite the large number of parameters and large number of multiplication (or division) operations, these models are efficiently implemented on FPGA platforms using fixed-point architectures. Detailed FPGA design process, hardware architecture and timing analysis are provided for three of the studied models (Ebola, Influenza, and Cancer) on an Altera Cyclone IV EP4CE115F29C7 FPGA chip. All models are also implemented on a high performance Xilinx Artix-7 XC7A100TCSG324 FPGA for comparison of the needed hardware resources. Experimental results showing real-time control of the chaotic dynamics are presented.

Stochastic SIR model predicts the evolution of COVID-19 epidemics from public health and wastewater data in small and medium-sized municipalities: A one year study

“…The unpredictable nature of the pandemic spread has been tackled, on the one hand from the perspective of deterministic chaos [14] , [15] , [16] and, on the other hand, using stochastic models [17] , [18] . Dynamic stochastic models for COVID-19 spread prediction can be broadly categorized into: (i) stochastic differential equations based in classical SIR models [8] , [17] , and (ii) compartmental models combined with Mote Carlo methods [6] , [19] , [20] , [21] .…”

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

“…There are many models introduced for pandemic disease, but in 2021, a covid model 24 was introduced by considering data taken from highly infected countries such as Italy, Japan, South Korea and China has got much importance. The considered model taken from 11 , 24 is given as : where , , shows the daily numbers of new cases, daily additional severe cases and new death cases, respectively. Mathematically, system ( 1 ) exhibits chaotic behavior for initial conditions (184, 30, 8) and parameter values given in Table 1 .…”

“…The degree of chaos and unpredictability in a system is determined by its sensitivity to the initial conditions, the bifurcation parameter, and the dense oscillatory solutions. The aforementioned features of chaos in continuous systems are increasing its appeal by using it as a transmitter in secure communication 1 , path planing problems 2 – 4 , cryptography 5 and motion control 6 but apart from these applications in engineering, the term ”chaos” continues to be associated with negative impact in biological models and still remain as a villain such as Cancer 7 , Ebola 8 , 9 , Influenza 10 , 11 , HIV 12 , 13 and Parkinson 14 epidemic diseases models.…”

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

“…Moreover, the research on covid-19 is not restricted to biology, but a lot of work can be found in other fields as well, such as, Machine learning [ 6 , 7 ], dynamical systems [ 8 , 9 ]. The covid-19 model [ 10 , 11 ] that we have considered is where , and shows the daily numbers of new cases, daily additional severe cases and new death cases reported per day due to covid, respectively. Mathematically, system ( 2 ) exhibits chaotic behaviour for initial conditions =(184, 30, 8) and parameter values given in Table 2 .…”

“…Moreover, the research on covid-19 is not restricted to biology, but a lot of work can be found in other fields as well, such as, Machine learning [6,7], dynamical systems [8,9]. The covid-19 model [10,11] that we have considered is…”