Development of an epidemiological model SEIasIsyIcrHpUicDthPiVacRS for human-pathogen interactions

The study presents a novel epidemiological model $SEI_{as}I_{sy}I_{cr}H_pU_{ic}D_{th}P_{i}V_{ac}RS$ to analyse the human-pathogen transmission dynamics by incorporating multiple parameters of human-pathogen interactions, multiple disease compartments, and vaccination effects. The model is governed by a system of differential equations and solved by exploring the fourth-order Runge-Kutta method. The impact of variation in the epidemiological parameters, such as transmission rates ($\beta_1, \beta_2, \beta_3$), vaccination efficacy ($\sigma$), and the proportion of asymptomatic cases ($\delta_{as}$), has been analyzed to understand the transmission and control of a viral disease. The model is an extension of an earlier study in which natural death rate, birthrate, vaccination, and re-susceptible cases were not incorporated in the earlier study. The model has been validated using a larger population dataset from Uttar Pradesh, India, compared to that of Kenya, by investigating the transmission dynamics of coronavirus across a wider range of compartments. The framework is also adaptable to other epidemic diseases like SARS, monkeypox, swine flu, influenza, etc. The observation in this study reveals that non-pharmaceutical interventions reduce transmission rates by $20-30$\% significantly delay infection peaks, reduce hospitalizations up to $71.7$\%, and alleviate health-care burdens. The study highlights the critical role of vaccination in mitigating severe outcomes, with higher coverage reducing symptomatic and critical cases. The findings emphasize the importance of early detection of asymptomatic carriers, dynamic public health policies, and healthcare system preparedness in controlling pathogen spread, providing intriguing perspectives on epidemic management in resource-limited settings. This study enhances pathogen spread understanding, identifies optimal controls, and supports dynamic policies like early asymptomatic detection and equity-focused vaccine distribution. The study also suggests future work on sensitivity analysis ($\tau_{as}$, $\lambda_{uic}$), ML/GIS hybrids for spatial/multi-strain modelling, and optimal control for low-resource cost-effectiveness.