# The North Carolina Journal of Mathematics and Statistics

### Analysis of a Vector-Borne Diseases Model with a Two-Lag Delay Differential Equation

#### Abstract

We are concerned with the stability analysis of equilibrium solutions for a two-lag delay differential equation which models the spread of vector-borne diseases, where the lags are incubation periods in humans and vectors. We show that there are some values of transmission and recovery rates for which the disease dies out and others for which the disease spreads into an endemic. The proofs of the main stability results are based on the linearization method and the analysis of roots of transcendental equations. We then simulate numerical solutions using MATLAB. We observe that the solution could possess chaotic and sometimes unbounded behaviors.

#### Keywords

delay differential equations; epidemiology; vector-borne diseases; linearization; transcendental equations; stability.

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#### References

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