Developing Insurance Mathematical Model to Assess Economic Burden of Dengue Outbreaks (Journal of Nonlinear Modeling and Analysis, 2024)
Dengue fever is a vector-borne viral disease that has become aworrisome health issue in tropical and subtropical countries. The seasonaltrend of dengue incidence encourages outbreaks with a high risk of infectionat particular periods annually that potentially resulted in a significant economic burden. The epidemiological mathematical model, the SIR-SI model, ismodified by considering the time-dependent and periodic-forced infection rateparameter through sinusoidal functions to obtain well data fitting. We showthe existence and the stability of the disease-free and endemic equilibria forthe system and their relation to the basic reproduction number of the disease.Next, we adapt the insurance concept to develop an insurance mathematicalmodel that accommodates the proposed dengue transmission model in calculating nominal premiums. An increase in the basic reproduction number asan important indicator of the level of disease transmission risk resulted in anincrease in the nominal premium. We also introduce a reserve function thatguarantees sufficient premium payments collected by insurer to cover up futureexpenditure due to dengue outbreaks. Through this reserve function, we obtain an adjusted premium as a minimum value of premium which ensures thatthe reserve function is always positive. Mathematical models combined withinsurance features have the potential to become important tools for relevantauthorities to gain insight into disease transmission dynamics as well as assessthe economic burden induced by the occurrence of disease outbreaks.
Keywords: Dengue; SIR model; insurance; economic burden; premium.