A Two-Strain Deterministic Dengue Model With Seasonality Effect

Abstract

A compartmental model is proposed to describe the dynamics of vector-host interations for dengue disease transmission with coexistence of two virus serotypes. The model is modified to incorporate  seasonal-dependent mosquito birth rate in order to examine the influence of climatic factors such as rainfall and temperature on the dynamics of mosquito population and dengue disease transmission. The Next Generation Matrix method is used to obtain the basic reproduction number associated with the model without seasonality effect. The global dynamics of the model is analysed using the Comparison Theorem. The model is simulated in MATLAB with ode45 routine for two cases, namely: the less aggressive case (Case ) and the more aggressive case (Case ).  Analysis of the model shows that the Disease-Free Equilibrium (DFE) is locally asymptotically stable whenever both the basic reproduction numbers  R01 (associated with strain  only) and  R0j (associated with strain  only) are below unity. It is shown that the DFE is globally asymptotically stable when the susceptibility indices for secondary infection in strain  1 ( sigma1) and strain j ( sigmaj), and  are all less than 1.