Convolutional modelling of epidemics

Traditional deterministic modeling of epidemics is usually based on a linear system differential equations in which compartment transitions are proportional to their population, implicitly assuming an exponential process for leaving as happens radioactive decay. Nonetheless, this assumption quite unrealistic since it permits class transition such the passage from illness recovery that does not depend time individual got infected. This trouble significantly affects evolution epidemy computed by these models. paper describes new epidemic model among different population classes described convolutional law connecting input and output fluxes each class. The guarantees changes always take place according realistic timing, defined impulse response function transition, avoiding decay typical previous contains five compartments can into consideration healthy carriers recovered-to-susceptible transition. provides complete mathematical description presents three sets simulations show its performance. A comparison with predictions SIR given. Outcomes simulation COVID-19 pandemic discussed predicts truly observed dynamic case-fatality rate. foresees possibility successive waves well asymptotic instauration quasi-stationary regime lower infection circulation prevents definite stopping epidemy. We existence quadrature formally solves convolutive models whose limit roughly matches basic reproduction number.