A Semi Analytical Solution to Two Strains Covid-19 Model with Vaccination and Awareness Program

Awareness and vaccination are important considerations in modelling the transmission dynamics of multiple COVID-19 strains. This study developed and analysed a deterministic model of two-strain COVID-19 transmission incorporating awareness and vaccination. The model comprised seven nonlinear differential equations describing transitions between epidemiological compartments. Positivity and boundedness of the model solutions were established. The disease-free equilibrium and the endemic equilibria associated with each strain were examined, and the conditions for the existence of the strain-specific endemic equilibria were derived analytically. Using available data, semi-analytical solutions were constructed through the Adomian Decomposition Method (ADM), yielding convergent series representations of the state variables as functions of time. Numerical simulations indicated that awareness reduced infections and increased vaccination rates within the model. The ADM solutions agreed with those obtained using the classical fourth-order Runge–Kutta method, supporting the numerical accuracy of the semi-analytical approximations. These findings demonstrate the utility of ADM for solving the proposed nonlinear transmission model and highlight the potential contribution of awareness to reducing infections and increasing vaccination rates in a two-strain setting.