EFFECTS OF VACCINATION AND SATURATED TREATMENT ON COVID-19 TRANSMISSION IN INDIA: DETERMINISTIC AND STOCHASTIC APPROACHES

This study explores an epidemic model elucidating the dynamics of COVID-19 transmission amidst vaccination and saturated treatment interventions. The investigation encompasses both deterministic and stochastic frameworks, considering constant and fluctuating environments, utilizing COVID-19 data from India for empirical validation. Through rigorous mathematical and numerical analyses, we ascertain pivotal insights. Our deterministic model unveils a critical phenomenon: the occurrence of backward bifurcation at R-0 = 1, underscoring that merely reducing the basic reproduction number below unity does not ensure disease eradication. Sensitivity analyses underscore the acceleration of epidemic spread with higher transmission rates, yet mitigation measures such as vaccination and comprehensive treatment can effectively reduce the basic reproduction number below unity. Within the stochastic framework, we establish the existence of a unique global positive solution. We delineate conditions for disease extinction or persistence and identify criteria for the emergence of stationary distribution, reflecting the sustained presence of infection within the community. Our findings elucidate that while smaller noise intensities sustain disease prevalence, heightened noise levels lead to complete eradication of the infection.