VCADS responds to Covid-19
  •   SEIR and SII model for the COVID-19 pandemic
    SEIR model for the COVID-19 pandemic:

    Compartmental modeling is an extremely general and versatile modeling approach. These models date back to the early 20th century. They are often used in the modeling of infectious diseases using nonlinear ordinary differential equations. The population is labelled into different compartments, such as S, I, or R. (Susceptible, Infectious, or Recovered) and people may move between compartments. As an example, SEIR stands for susceptible, exposed, infected, and recovered, and it indicates the flow patterns between the compartments.

    These models aim to estimate various epidemiological characteristics, such as the reproduction number, and provide predictions about the spread of a disease, the total number of infected, the length of an epidemic, and other variables. These models can illustrate the potential impact of various public health initiatives on the course of an epidemic.

    Fig. 1 (a) Infected versus reproduction number for different values of government actions. (b) Infected versus reproduction number for different values of public behavior.In one of our recent studies, we have developed an SEIR model for the COVID-19 pandemic that considers governmental intervention imposed, social behavior and public response to the rules imposed.This work demonstrates how two key sociological variables—public perception and governmental policy can have a major impact on the disease transmission rate and its pattern of spread. The study shows that more aggressive government measures and regulations (Fig. 1 a), such as quarantines, mask use, social distancing, and enhancing public perception (Fig. 1 b), may be necessary to stop the spread of COVID-19.


    SII model for the COVID-19 pandemic:

    In another work, we have developed an SII (susceptible, infected, immune) model to demonstrate the periodic behavior of the pandemic and effect of the perfect and imperfect vaccination on the pandemic. The periodic behavior is explained incorporating the first harmonic approximation of transmission rate.

    The figures shown below show Backward bifurcation phenomenon due to imperfect vaccination, Response of the system under perfect vaccination, Response of the system under imperfect vaccination.

    This work demonstrates the fact that imperfect vaccination leads to a saddle-node bifurcation where the stable disease-free equilibrium transfers into an unstable endemic equilibrium. This phenomenon is called backward bifurcation and occurs under imperfect vaccination. The main reason is the fact that imperfect vaccination creates two subclasses of susceptible individuals with different susceptibilities: the naive susceptible and the vaccinated susceptible. This is one of the principal reasons for the persistent dynamic behavior of the COVID-19 epidemic.

    The research shows that the amplitude of the transmission rate determines the peak of the infected population while the frequency and phase of the transmission rate determine the persistence of the disease. These results support the hypothesis that the dynamic behavior of an endemic disease like COVID-19 is influenced by factors including imperfect vaccination, environmental factors, and new viral mutants. The dynamic behavior of the disease is also influenced by social and biological factors auch as population density, social isolation policies, and governmental actions.

    Finally, and most crucially, our study implies that boosting vaccination rates, enhancing vaccine efficacy, and enacting public policies would decrease oscillatory behavior and aid in the full eradication of the disease.

  •  Article by Dr. Nataraj on the value of mathematical modeling to define policy

    Natural catastrophes are a lot scarier than the ones we engender (for example, a car accident) because of the lack of precise understanding we have about them and the cloud of uncertainty that seems to surround them. Their magnitude, impact and the predictability of future evolution all seem uncertain, which further leads to a sense of helplessness as these events seem to be out of our control while our engineered lives seem to be mostly controllable.Read more here