Abstract
In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a nonmonotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to [Formula: see text] and the epidemic growth rate. Local stability of endemic equilibrium is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when [Formula: see text] although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bistable dynamics. However, efficient application of temporary control in bistable regions will curb the disease to lower endemicity. Additionally, numerical simulations reveal that the equilibrium level of infected hosts decreases as psychological effect increases.
Highlights
181 sensitivity indices of R0 with respect to the parameters βd and βi. In this case, increasing the parameters βd and βi by 1%, the value of R0 increases by 0.9952% and 0.0048;% respectively. These results suggest that the direct transmission pathway is more sensitive to epidemic growth rate (EGR) and R0 than the indirect one, which indicates that the direct transmission control will be more effective in halting the early phase of the
We find that our model exhibits a hysteresis effect where multiple 433 endemic equilibrium coexist for R0 > 1
We can employ temporary control interventions to push the solution into the basin of attraction of the disease free equilibrium (DFE). in case of hysteresis, these control measures will compel the solutions to the basin of attraction of the lower endemic equilibrium
Summary
21 policies have been found very effective [5; 6] in decreasing the rate of infection at the late stage of SARS. Ruan and Wang [8] studied an SIRS epidemic model with a specific nonlinear incidence rate g(I)S βI2S 1+αI 2. Afterwards, Xiao and Ruan [9] studied the dynamical behaviour of an SIR epidemic model with the incidence function g(I )S βIS 1+αI. 33 the dynamics of an epidemic model with two transmission routes where the direct trans-. 35 and zika virus epidemic are examples of diseases with two routes of transmission having psychological. There is a negative correlation between the psychological effect and disease prevalence and we consider non-monotone incidence function i.e. p < q to describe the direct transmission between hosts in our study. We use the incidence rate g(I )S βIS 1+αI 2 where βI represent the force of infection of the diseases,. By using analytical methods we intend to uncover the dynamical properties of the 49 diseases with two routes of transmission
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