Abstract
Problem statement: In 2008 there was a large outbreak of Chikungunya fever in southern Thailand. Chikungunya fever is an emerging disease which tends to affect rubber plantation and fruit orchard workers more than other occupation. This study we considers the efficacy of using mosquito repellent as a way to prevent and control the spread of Chikungunya fever. The mathematical model of the dynamic of this disease is proposed and analyzed. Approach: A standard dynamical modeling method was applied for analysis the dynamical model. The stability of the model was determined by using Routh-Hurwitz criteria. Results: The conditions for disease free and endemic state are found. To determine the basic reproductive number (R0) which is the threshold parameter, if R0 1, there exist the endemic equilibrium state, which is locally asymptotically stable. Conclusion: It was found that the use of mosquito repellent significantly reduce transmission and infection of this disease which it may be an alternative intervention for communities to prevent and control the disease.
Highlights
Numerical results: In this study, we are interested in the transmission of Chikungunya fever with the effect of efficacy of mosquito repellent for protecting the mosquito
Stability of disease free state: From the values of parameters listed in Table 1, we obtained the eigenvalues and basic reproductive number is: λ1 = −0.151962,λ2 = −0.133737, λ3 = −0.000042, R0 = 0.004069 < 1 (b)
The solutions converge to the disease free equilibrium state as shown
Summary
Sm (Im) = The number of susceptible (infected) mosquito population λh, (μh) = The birth (death) rate of human population. = The transmission rate of CHIKV from infected mosquito to human population:. Where, γmh is the transmission rate of CHIKV from infected human to mosquito population:. To determine the other eigenvalues from the characteristic equation λ2 + A1λ + A2 = 0 The root of this equation is negative if it is satisfied with two conditions of Routh-Hurwitz criteria. Disease endemic equilibrium point: To determine the stability of the endemic equilibrium point, E1, by finding the eigenvalues of Jacobian matrix at E1, as follow: the is E1(S*h , I*h , I*m ).
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