Hosein Taheri - Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, ۵۶۱۹۹-۱۱۳۶۷, Ardabil, Iran
Nasrin Eghbali - Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, ۵۶۱۹۹-۱۱۳۶۷, Ardabil, Iran
Masoumeh Pourabd - Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, ۱۸۴۱, Rasht, Guilan, Iran

Kermack-McKendrick-type epidemic models are commonly used for modeling epidemic diseases. In this study, we have proposed a Kermack-McKendrick-based model to elucidate the impact of COVID-۱۹ vaccination on the spread of the virus in Iran. This model serves as an endemic assessment tool, tailored to fit reported data in Iran, for gauging the potential population-level effects of the COVID-۱۹ vaccine. It's important to note that COVID-۱۹ vaccines do not guarantee complete protection against the disease. A vaccinated person may still become infected, highlighting the necessity of continuous vaccination while an individual is in the system. To address this, we considered two models—one with only one strain and the other containing two strains. We hypothesize that the vaccine results in complete immunization against one strain while conferring partial immunization against the other. To explore this, we consider two scenarios. In the first scenario, we assume that the vaccine does not provide complete immunity, and individuals may become infected again after vaccination. In the second scenario, a dual-strain model is considered, positing that individuals, when vaccinated, remain immune to the strain present in the vaccine, but are susceptible to another strain for which the vaccine provides partial protection. However, this other strain may still lead to infection in individuals. The analysis of the proposed models revealed that where the prevalence rate, or the basic reproduction number (R۰) - an index measuring the spreading potential of a pathogenic agent and the average number of individuals each infected person can potentially transmit the infectious agent to susceptible individuals - has a direct correlation with vaccination. Therefore, to assess the extent of vaccine efficacy, this indicator is employed, with a lower prevalence rate being the targeted outcome.

Coronavirus pandemic globally, COVID-۱۹ coronavirus, Mathematical modeling of infection disease, SEIRUS-model, Parameter identification, Vaccination, Herd Immunity