Modelling of contact tracing in determining critical community size for infectious diseases

Abstract

In large communities, persistence of any epidemic eruption continues for a long time and the eradication of the epidemic is too critical as it depends on many affecting variables. In case of disease prevalence in small communities, critical community size (CCS), a threshold, helps to convey prediction about the expected time to extinction of any epidemic. We propose a deterministic model of HIV/AIDS epidemic considering the role of contact tracing in HIV partner notification. The stochastic version of our proposed model aids us to compute the CCS and time to extinction of HIV/AIDS epidemic. The model is adjusted using the data of HIV/AIDS cases of India for the last 30 years and key parameters are estimated. The sensitivity analysis enables to identify the influence of the model parameters in controlling the HIV/AIDS epidemic. Our computation approach is independent of number of variables and thus may be fitted in determining the critical community size for any infectious disease (with the tend to persist for indefinite time) model with complex dynamics or of higher order.