Covid-19

Mathematical Modelling of Covid-19 using modified SEIRS Model

Default parameters

Transmission rate (β)		ℹTransmission rate is the probability of transmitting disease between a susceptible and an infectious individual
Birth rate (μ)		ℹRatio of number of births in one year to the total population
Death rate (λ)		ℹRatio of number of deaths in one year to the total population
Proportion of vaccinated population (V)		ℹRatio of the vaccinated population to the total population.
Proportion of non vaccinated population (NV)		ℹRatio of the non-vaccinated population to the total population.
Rate of movement from Exposed with vaccinated to Infected with symptomatic (σ_SV)		ℹRatio of number of individuals moved from E_V to I_S per day to the population of E_V
Rate of movement from Exposed with vaccinated to Infected with asymptomatic (σ_AV)		ℹRatio of number of individuals moved from E_V to I_AS per day to the population of E_V
Rate of movement from Exposed with non vaccinated to Infected with symptomatic (σ_SNV)		ℹRatio of number of individuals moved from E_NV to I_S per day to the population of E_NV
Rate of movement from Exposed with non vaccinated to Infected with asymptomatic (σ_ANV)		ℹRatio of number of individuals moved from E_NV to I_AS per day to the population of E_NV
Death rate from Infected with symptomatic compartment (α_S)		ℹRatio of number of deaths from I_S per day to the population of I_S
Death rate from Infected with asymptomatic compartment (α_AS)		ℹRatio of number of deaths from I_AS per day to the population of I_AS
Recovery rate from Infected with symptomatic compartment (γ_S)		ℹRatio of number of individuals recovered from I_S per day to the population of I_S
Recovery rate from Infected with asymptomatic compartment (γ_AS)		ℹRatio of number of individuals recovered from I_AS per day to the population of I_AS
Rate of losing immunity against the disease (ω)		ℹRatio of number of individuals in R losing immunity per day to the population of R
Total time steps (days) to display		ℹTotal number of time (days) to display the graphs

Input values

Choose varying parameter and enter three values Enter the inital values for each class

Susceptible (S)

Exposed with vaccinated (E_V)

Exposed with non vaccinated (E_NV)

Infected with symptomatic (I_S)

Infected with asymptomatic (I_AS)

Recovered (R)

SEIRS Compartmental model

Mathematical representations of infectious diseases include compartment-based SEIR and SEIRS models. These models are represented using coupled differential equations that capture the flow of populations from one compartment to another. While these models have been used for several infectious diseases such as HIV/AIDS, tuberculosis, Dengue fever, and COVID-19, the models do not generally incorporate compartments for vaccinated populations, asymptomatic infections, and the possibility of reinfection.

This modified Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) compartment model for COVID-19 disease incorporates the compartments for exposed vaccinated and non-vaccinated populations, and those with symptomatic and asymptomatic infections. In this work, we present a modified SEIRS model that consists of six compartments:

Susceptible
Exposed to vaccination
Exposed with non-vaccination
Infected persons with symptoms
Asymptomatic infected
Recovered

Transition diagram of modified six compartmental SEIRS model to predict the infections of disease spread.

The modified SEIRS model can be represented using a set of coupled differential equations:

𝑑𝑠/𝑑𝑡 = 𝜇𝑁+ 𝜔𝑅 − 𝜆𝑆 − ((𝑉𝛽𝐼_S 𝑆)/𝑁) − (((𝑁𝑉)𝛽𝐼_S 𝑆)/𝑁)

(𝑑𝐸_V)/𝑑𝑡 = ((𝑉𝛽𝐼_S𝑆)/𝑁) − (𝜆 + 𝜎_𝑆𝑉 + 𝜎_𝐴𝑉)𝐸_V

(𝑑𝐸_NV)/𝑑𝑡 = (((𝑁𝑉)𝛽𝐼_S𝑆)/𝑁) − (𝜆 + 𝜎_𝑆𝑁𝑉 + 𝜎_𝐴𝑁𝑉)𝐸_NV

(𝑑𝐼_S)/𝑑𝑡 = 𝜎_SV𝐸_V + 𝜎_𝑆𝑁𝑉 𝐸_𝑁𝑉 − (𝜆 + 𝛼_S + 𝛾_𝑆)𝐼_S

(𝑑𝐼_AS)/𝑑𝑡 = 𝜎_𝐴𝑉𝐸_V + 𝜎_𝐴𝑁𝑉𝐸_𝑁𝑉 − (𝜆 + 𝛼_𝐴𝑆 + 𝛾_𝐴𝑆)𝐼_𝐴𝑆

(𝑑𝑅)/𝑑𝑡 = 𝛾_S𝐼_S + 𝛾_𝐴𝑆𝐼_𝐴𝑆 − (𝜆+𝜔)𝑅

where
λ is the natural death rate
μ is the natural birth rate
β is the contact rate
V is the fraction of the population vaccinated against the infectious disease
NV is the fraction without the vaccine so that V + NV = 1
α_S and α_AS are the death rates due to the infectious disease for symptomatic and asymptomatic infections, respectively
γ_S and γ_AS are the recovery rates for the symptomatic and asymptomatic infections, respectively
σ_SV , σ_SNV , σ_AV , σ_ANV are the rates of transition from exposed to infected compartments
ω is the fraction of recovered persons who lose immunity and become susceptible to infection again