Host-vector interaction in dengue: a simple mathematical model

Dengue is a mosquito-borne viral infection endemic in tropical and subtropical regions, now spreading at epidemic proportions causing a major health issue in Sri Lanka and elsewhere. No effective vaccine or a curative antiviral drug is available to prevent or treat the disease. The only way of mitigating dengue at present, is through mosquito eradication and educating the public on preventive measures which can minimizing the cycle of transfer.

A theoretical model of dengue with simple mathematics is presented to gain a quantitative understanding of the pattern of dengue outbreaks in Sri Lanka and suggest control measures.

The statistics on incidence of the disease reported by the Epidemiology Unit is analyzed using the model. Despite simplicity, the model possesses explanatory and predictive capacity, enabling determination of crucial parameters. The model shows that the “infectives” increase exponentially in an outbreak, provided the number of vectors per human exceeds a threshold, illustrating not only vector eradication but measures which minimize their biting frequency and preventing prolonged survival are effective safeguards.

In a population consisting of 75% who are susceptible, the threshold is estimated to be 20 mosquitos per person.

The model showed that the endemic equilibrium of the system can occur at any level. As demographic changes escalate mosquito breeding, they infect more and more susceptible people. The consequent increase in virus replication induces new strains broadening the genetic diversity of the virus and helping it to overcome the human immune response. The increasing endemicity of dengue due to this is demonstrated by the model.