Abstract
Dengue fever is a common disease which can cause shock, internal bleeding, and death in patients if a second infection is involved. In this paper, a multi-serotype dengue model with nonlinear incidence rate is formulated to study the transmission of two dengue serotypes. The dynamical behaviors of the proposed model depend on the threshold value R_{{0}}^{{n}} known as the reproductive number which depends on the associated reproductive numbers with serotype-1 and serotype-2. The value of R_{{0}}^{{n}} is used to reflect whether the disease dies out or becomes endemic. It is found that the proposed model has a globally stable disease-free equilibrium if R_{{0}}^{{n}}leq 1, which indicates that if public health measures that make (and keep) the threshold to a value less than unity are carried out, the strategy in disease control is effective in the sense that the number of infected human and mosquito populations in the community will be brought to zero irrespective of the initial sizes of sub-populations. When R_{{0}}^{{n}}>1, the endemic equilibria called the co-existence primary and secondary infection equilibria are locally asymptotically stable. The effects of cross immunity and nonlinear incidence rate are explored using data from Thailand to determine the effective strategy in controlling and preventing dengue transmission and reinfection.
Highlights
Dengue is a viral mosquito-borne infection which in recent years has become a major international public health concern, a leading cause of illness and death in the tropics and subtropics with more than 50 million dengue fever cases per year [1, 2]
Anggriani et al.[26] studied the effect of reinfection with the same serotype on dengue transmission dynamics by developing a multi-strain dengue mathematical model, which suggested that reinfection with the same serotype may be one of the underlying factors causing an increase in the number of secondary infections
To ensure the effective disease control of both primary and secondary dengue infections, it is imperative to show that the disease-free equilibrium (DFE) is globally asymptotically stable (GAS) in order to make sure that the number of infected cases in the community at steady state are independent of the initial sizes of the sub-populations of a multi-serotype dengue model
Summary
Dengue is a viral mosquito-borne infection which in recent years has become a major international public health concern, a leading cause of illness and death in the tropics and subtropics with more than 50 million dengue fever cases per year [1, 2]. Anggriani et al.[26] studied the effect of reinfection with the same serotype on dengue transmission dynamics by developing a multi-strain dengue mathematical model, which suggested that reinfection with the same serotype may be one of the underlying factors causing an increase in the number of secondary infections. A mathematical model of dengue fever epidemiology with two serotypes is constructed by incorporating cross immunity and nonlinear incidence rate to explore the risk of secondary infection. To ensure the effective disease control of both primary and secondary dengue infections, it is imperative to show that the DFE is globally asymptotically stable (GAS) in order to make sure that the number of infected cases in the community at steady state are independent of the initial sizes of the sub-populations of a multi-serotype dengue model.
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
