A modified SIR model to study on physical behaviour among smallpox infective population in Bangladesh

The susceptible infected removal (SIR) model is widely used in epidemiology and public health to compute number of individuals in each categories of the population, and to explain the change in the number of people needing medical attention during an epidemic as well as evaluate policies effectively during the epidemic. Some extensions of this model have been studied and findings demonstrated that there exists a large class of functions representing interacting between the susceptible and infective population for which the model has realistic behavior and preserves the essential factures of the classical model. In this study we propose a new modification of SIR epidemic model to examine the appropriateness of the policies taken to control or eradicate disease with an application to smallpox data. The solutions of the parameters for our proposed model showed a very realistic behavior. In particular, the solutions have demonstrated that the number of infective people increases significantly during an initial period of the epidemic and then decreases and remain stable over the rest of the time. The temporal behavior of infectives for smallpox disease has been considered as an example within the modified frame work and the smallpox data from 1950 to 1977 in Bangladesh have been fitted by taking care of the model coefficients which are applied to estimate prediction of the infective population. Results revealed that the infectives curve of smallpox for the modified model has systematic noticeable variation over time, and the predicted numbers of infectives remain consistent for the next five years. Infection free and most critical periods are distinguishable in the results so that the local and international health systems can act accordingly and provide emergency and regular supports during the critical period of a smallpox epidemic. This modified model can further explore underlying factors for smallpox disease as a basis to generate hypotheses on potential determinants of smallpox in Bangladesh and worldwide contexts. It can also be applicable for the prediction of other infectious diseases.