Table 1 Variables and parameters descriptions
\(S(t)\) Susceptible population at given time t |
\(V(t)\) Vaccinated population at given time t |
\(E(t)\) Those that were exposed at given time t |
\(I(t)\) Symptomatic and infectious individuals in the population at given time t |
\(P(t)\) Super-spreader population at time given t |
\(A(t)\) The infected but asymptomatic population at time t |
\(H(t)\) Hospitalized population at time t |
\(R(t)\) Recovering population at time t |
\(F(t)\) Dead or fatality class population |
\(\pi\) Recruitment rate |
\(K_{1} I(t)S(t) + K_{2} H(t)S(t) + K_{3} P(t)S(t)\) is force of infection |
\(\beta\) Measures human-to-human transmission coefficient |
\(\beta^{^{\prime}}\) Measures transmission coefficient of a super-spreader |
\(l\) measures the relative transmission risk of hospitalized individuals |
\(\kappa\) the rate in which people leave the exposed class |
\(\rho\) The rate at of recruiting the vaccinated individual |
\(\omega\) The rate of losing the vaccination |
\(\delta_{v}\) The death rate due to the vaccination |
\(\rho_{1}\) fraction of change from exposed class to symptomatic |
\(\rho_{2}\) Comparatively less people become super-spreaders when they are exposed |
\(1 - \rho_{1} - \rho_{2}\) from the exposed to the asymptomatic class |
\(\gamma_{a}\) the standard hospitalization rate for symptomatic super-spreader individuals |
\(\gamma_{1}\), \(\gamma_{r}\) Hospitalized recovery rate |
\(\delta_{i}\), \(\delta_{p}\), \(\delta_{h}\) Infected, super-spreader, and hospitalized populations' relative disease-related death rates |