Complex Temporal Behaviour Modeling for Pandemic Spread: Not a Simple Delayed Response!

One of the significant challenges, when a new virus circulates in a host population, is to detect the outbreak as it arises in a timely fashion and implement the appropriate preventive policies to effectively halt the spread of the disease. The conventional computational epidemic models provide a state-space representation of the dynamic changes of various sub-clusters of a society based on their exposure to the virus and are mostly developed for small-size epidemics. In this work, we reshape and reformulate the conventional computational epidemic modeling approach based on the complex temporal behavior of disease propagation in host populations, inspired by the COVID-19 pandemic. Our new proposed framework allows the construction of transmission rate (p) as a probabilistic function of contributing factors such as virus mutation, immunity waning, and immunity resilience. Our results unravel the interplay between transmission rate, vaccination, virus mutation, immunity loss, and their indirect impacts on the endemic states and waves of the spread. The proposed model provides a robust mathematical framework that allows policy-makers to improve preparedness for curtailing an infectious disease and unfolds the optimal time-frame for vaccination given the available resources and the probability of virus mutation for the current and unforeseen outbreaks.