Uncovering the influence of public awareness on dengue population dynamics: a mathematical model approach

Abstract

An arbovirus belonging to the Flaviviridae family is the cause of the infectious disease called dengue fever. In this work, the human population is divided into eight compartments, which are (S-h) indicates susceptible people, (E-h) indicates dengue virus-exposed humans, Controlled humans (C-h) are those who are aware of the dengue virus and how humans can get infected with it. People infected with the dengue virus are known as infectious humans (Ih), and they can spread the illness to others by being bitten by mosquitoes. Treated individuals (T-h) these are humans that are undergoing treatment, Recovered individuals (R);These are individuals that are recovered from the disease, Susceptible vectors (S-v);these are susceptible mosquitoes that can be contracted with virus by biting infected humans, Infected vectors (I-v) these are infected mosquitoes that are capable of transmitting the virus to human by bite. Among the other things done: the boundedness of the model has been ascertained, and the threshold called reproduction number R-c has been obtained using a new generation matrix. The existence of equilibria has been ascertained, which showed that the model consists of two equilibria, the disease-free equilibrium point (DFE) and endemic equilibrium point. Local stability of disease-free equilibrium has been ascertained, which showed that the DFE is locally asymptotically stable if R-c< 1 and unstable otherwise. The global stability of disease-free equilibrium has been ascertained using the comparison theorem, the significance of this method is that is easier to access the global stability of disease-free equilibrium with it and it is faster. The global stability of the endemic equilibrium point has been ascertained using the non-linear Lyapunov function of the Go-Volterra type, the result shows that the endemic equilibrium point is globally asymptotically stable if R-c> 1, when recovered individuals does not whine, exposed and infected individuals does not recover that is when pi = kappa(1) = kappa(2) = 0 and unstable otherwise. The sensitivity analysis shows that the effective contact rate of humans is the most sensitive in increasing the control reproduction number while the awareness rate is the most sensitive in decreasing the control reproduction number. The simulation result shows that public awareness is a very important technique to control dengue fever in society.