FINAL SIZE RELATIONS FOR SOME COMPARTMENTAL MODELS IN EPIDEMIOLOGY

The summary measurement of an epidemic such as the final size is an important quantity that allows us to approximate the impact of the disease on the affected region. In recent years, final size measurements for vector-transmitted diseases have acquired importance because of the increased concern for mosquito-borne diseases like dengue, Zika, Chikungunya, etc. However, analytical expressions for this estimate in the stage-structured models applicable to vector-borne diseases are less, mostly focused on the classical Kermack–McKendrick model. In this paper, we first calculate the final size expressions for an SIR model with carrier state and a SEIR–SI host–vector model. Then we extend this for the SEIR–SI host–vector model with treatment class in the host, as well as for the model with vertical transmission in the vector population. Finally, we verify our final size expression with some real scenarios.