Mathematical model of zika virus dynamics with vector control and sensitivity analysis

Abstract

In this paper, we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death. To formulate the model, we assume that the Zika virus is being first transmitted to human by mosquito bite, and then it is being transmitted to his or her sexual partner. The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points, exists under certain conditions. The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one. Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one. The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value. We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia. Furthermore, using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate, recruitment rate of mosquito, transmission probability per biting of Susceptible (infected) humans with infected (susceptible) mosquito, rate of awareness in host population, recovery rates of infected human are most sensitive parameters of the considered Zika model. Lastly, some conclusions are given to control the spreading of the Zika disease.

COVID-19 pandemic in India: a mathematical model study

“…In order to determine such parameters, we shall estimate sensitivity index of the basic reproduction number with respect to different parameters. Using the normalized forward sensitivity method [ 25 , 26 ], we have obtained sensitivity index , where is the characteristic parameter whose sensitivity on has to be determined. The calculated sensitivity indices with respect to each of the model parameters using both sets of parametric values have been presented in the last column of Tables 2 and 3 , respectively.…”

Dynamics of Botnet Propagation in Software Defined Networks Using Epidemic Models

“…Said information, analysis and evaluation can be also applied to understand and prevent malware proliferation within communication networks such as SDN. Most human epidemics in the literature follow the compartment modelling approach [5], [6], [10]- [14], [41]- [45], in which the affected population moves within a finite number of discrete states as shown in Figure 1.…”

Analysis the Dynamics of SIHR Model: Covid-19 Case in Djibouti

“…then one of the eigenvalues of the Jacobin matrix corresponding to the system (1) at DFE is zero. Using the Theorem by Castillo-Chavez and Song [18,19,20] to investigate the nature of the disease free equilibrium points. Let V d and V g be the eigenvector corresponding to the zero eigenvalue of J(E 0 ) and [J(E 0 )] T respectively then…”