Dynamic model of COVID-19 disease with exploratory data analysis

Abstract

Novel Coronavirus is a highly infectious disease, with over one million confirmed cases and thousands of deaths recorded. The disease has become pandemic, affecting almost all nations of the world, and has caused enormous economic, social and psychological burden on countries. Hygiene and educational campaign programmes have been identified to be potent public health interventions that can curtail the spread of the highly infectious disease. In order to verify this claim quantitatively, we propose and analyze a non-linear mathematical model to investigate the effect of healthy sanitation and awareness on the transmission dynamics of Coronavirus disease (COVID-19) prevalence. Rigorous stability analysis of the model equilibrium points was performed to ascertain the basic reproduction number R ₀, a threshold that determines whether or not a disease dies out of the population. Our model assumes that education on the disease transmission and prevention induce behavioral changes in individuals to imbibe good hygiene, thereby reducing the basic reproduction number and disease burden. Numerical simulations are carried out using real life data to support the analytic results.

Keywords: Education; Exploratory data analysis; Hygiene; Reproduction number; Stability.

Fig. 1

Diagram of an Isolated Corona virus, Pilch, R. (2020). World War : The COVID-19 Pandemic. Director, CNS Chemical and Biological Weapons Nonproliferation Program. Middlebury Institute of International Studies at Monterey. Available at https://www.nonproliferation.org/world-war-v-the-covid-19-pandemic/. Accessed on April 1, 2020.

Fig. 2

Schematic diagram of model dynamics between humans under the influence of Education.

Fig. 3

Correlation between Basic Reproduction Number R₀ and Sensitive parameters of the model.

Fig. 4

Simulations of system (2.6) for the total human population level as a function of time for R₀ < 1 with parameters set at $\gamma =0.052,{\Lambda }_T=0.02461,{\Lambda }_B=0.0072,H_0=0.0246,{\beta }_{\max }=0.0001,{\beta }_{\min }=0,p_1=0.0016,{\alpha }_1=0.062,{\alpha }_2=0.00403,{\alpha }_3=0.547,\sigma =0.0087,d=0.975,\mu =0.000182,\delta =0.4351,{\omega }_0=1,{\omega }_1=0.9495,{\omega }_2=0.0263$.

Fig. 5

Simulation showing the impact of Education on Susceptible, Quarantined, Infected and Recovered human populations over time with parameters set $\gamma =0.052,{\Lambda }_T=0.02461,{\Lambda }_B=0.0072,H_0=0.0246,{\beta }_{\max }=0.0001,{\beta }_{\min }=0,p_1=0.0016,{\alpha }_1=0.062,{\alpha }_2=0.00403,{\alpha }_3=0.547,\sigma =0.0087,d=0.975,\mu =0.000182,\delta =0.4351,{\omega }_0=1,{\omega }_1=0.9495,{\omega }_2=0.0263$.

Fig. 6

Simulation showing the impact of good Hygiene (H) on Susceptible, Quarantined, Infected and Recovered human populations over time with parameter set $\gamma =0.052,{\Lambda }_T=0.02461,{\Lambda }_B=0.0072,{\beta }_{\max }=0.0001,{\beta }_{\min }=0,p_1=0.0016,{\alpha }_1=0.062,{\alpha }_2=0.00403,{\alpha }_3=0.547,\sigma =0.0087,d=0.975,\mu =0.000182,\delta =0.4351,{\omega }_0=1,{\omega }_1=0.9495,{\omega }_2=0.0263$.

Fig. 7

Time Plots of COVID-19 situation in Italy.

Fig. 8

Histogram and Density Plots of COVID-19 situation in Italy.

Fig. 9

Box Plots of COVID-19 situation in Italy.

Fig. 6.1

Italy Data.