Abstract
Global incidence of dengue, a vector-borne tropical disease, has seen a dramatic increase with several major outbreaks in the past few decades. We formulate and analyze a stochastic epidemic model for the transmission dynamics of a single strain of dengue virus. The stochastic model is constructed using a continuous time Markov chain (CTMC) and is based on an existing deterministic model that suggests the existence of a backward bifurcation for some values of the model parameters. The dynamics of the stochastic model are explored through numerical simulations in this region of bistability. The mean of each random variable is numerically estimated and these are compared to the dynamics of the deterministic model. It is observed that the stochastic model also predicts the co-existence of a locally asymptotically stable disease-free equilibrium along with a locally stable endemic equilibrium. This co-existence of equilibria is important from a public health perspective because it implies that dengue can persist in populations even if the value of the basic reproduction number is less than unity.
Highlights
Dengue, a vector transmitted disease, has seen a dramatic increase in global incidence over the past decades [1,2]
This co-existence of equilibria is important from a public health perspective because it implies that dengue can persist in populations even if the value of the basic reproduction number is less than unity
The stochastic model is based on an existing deterministic model proposed by Garba et al [11] with one minor but important difference: contrary to the original deterministic model [11] and in line with previous studies of dengue virus such as [12,13], we will assume that exposed hosts and exposed vectors do not transmit the disease
Summary
A vector transmitted disease, has seen a dramatic increase in global incidence over the past decades [1,2]. This phase lasts for one or two days and is marked by low blood pressure, leakage of blood plasma from the capillaries and decreased blood supply to organs Severe cases of these symptoms are associated with DHF and DSS and the mortality in this phase of the disease is estimated to be as high as 5% 15% [3,5,8,9]. The stochastic model is based on an existing deterministic model proposed by Garba et al [11] with one minor but important difference: contrary to the original deterministic model [11] and in line with previous studies of dengue virus such as [12,13], we will assume that exposed hosts and exposed vectors do not transmit the disease. We conclude the paper by presenting a discussion of various directions in which to extend the current study
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
