Abstract
Many mathematical models developed through differential equations to describe the age dependent infectiousness of diseases, face the complexity of modelling heterogenic behavior of transmission. There, many of the cases assume the host to stay in the same risk class regardless of the age of the hosts. The proposed model mimics the infectiousness according to the age-scale of an individual via integral equation approach. This model indicates the applicability of Fredholm type integral equations with degenerated kernel. Introducing biological, behavioral and environmental influences provokes to address the accumulating nature of different factors in modelling the risk of getting infected. The risk of getting infected is modeled by the inability of responding with acquired immunity and the accumulated risk given from the other individuals in each age group via the mobility patterns. Within this approach environmental stimulus are modeled via periodic functions in order to describe the stochastic behavior of the spreading capabilities. In this study, the behavioral analysis evaluates the maximum risk of getting infectious in the considered parsimonious approach. And the sensitivity analysis describes the contribution of the mobility risk and stochastic nature on the overall risk. Further the model guides to formulate hypotheses and data collection strategies to measure the risk of a disease.
Highlights
In an epidemiological and public health standpoint, riskstructured susceptible-infected–recovered (SIR) models provide many insights into the dynamics of infections
This study focuses to mimic the infectiousness according to the age-scale
Summary
In an epidemiological and public health standpoint, riskstructured susceptible-infected–recovered (SIR) models provide many insights into the dynamics of infections. The individuals in their late teenage to Mathematical Modelling and Applications 2019; 4(1): 10-14 twenties tends to be more vulnerable in getting into infections due to day-to-day mobilization [2,3,4]. It is a key factor in behavioral influence. The proposed integral equation approach differs from usual SIR models due to the sequential progression through age It requires only one type of equation to incorporate acquired immunity and mobility along with some external stimuli behavior. It would illustrate general behavior of infectiousness occurring as an accumulated process
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