Mathematical Modelling and Analysis of Dengue Transmission Dynamics
Harshit, Priyanka Harjule
Abstract
Understanding and resolving the complexity of diseases such as dengue need the use of mathematical modelling, which enables us to forecast outbreaks, create practical solutions, and allocate resources effectively to lessen the disease's effects. This research proposes a mathematical model that examines the dynamics of dengue illness transmission. Te model accounts for a number of important factors that affect the disease's spread, including the increase of the mosquito population, how long it takes an illness to develop and the extent to which infected humans also infect mosquitoes. Further, basic reproduction number has been calculated using the next generation matrix method for the single strain dengue model and SEIR-SEI model has been analyzed via mathematical theorems showing the positivity of the solutions and boundedness of the equations governing the proposed model. Sensitivity analysis has been done for basic reproduction number R0. Te findings indicate that the basic reproduction number primarily depends on factors such as the transmission rate of disease and the rate at which mosquitoes become infected by infectious human beings and depends inversely on factors such as the recovery rate of humans and the rate at which mosquitoes transmit the virus to humans. Numerical simulations have been done on a small population to show the number of people and number of mosquitoes in different compartments at any given time t and it shows the progress of disease transmission in a population.