Capturing ‘superspreading’ in matrix models for vector-borne diseases

The terms R and ‘superspreader’ are often used in the context of the COVID pandemic. R, or basic reproduction number, is roughly speaking the number of new cases per infected case. It is a threshold value; if R is larger than 1, the disease will (continue to) spread(1). R can be calculated using matrix models.

Superspreaders are individuals that cause many more new cases than the average infected individual. This skewed distribution is common in infectious diseases; a large proportion of the transmission events is caused by a small subset of the infected individuals. Transmission often follows the pareto-principle (or 80-20 rule): about 80% of the transmission stems from 20% of the cases2.

In vector-borne diseases, which are transmitted by bites of mosquitoes, ticks, and other blood-feeding arthropods, heterogeneity in the number of bites is an important source of heterogeneity in transmission potential: a majority of the bites is taken on a minority of the hosts (Figure 1). This aggregation of bites over hosts strongly affects disease transmission dynamics: hosts that receive more bites, are a) more likely to be infected and b) more likely to transmit pathogens to a larger number of vectors. In this project, the effect of including heterogeneity in transmission in R0 matrix models will be investigated.

  1. Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28, 365–382 (1990).
  2. Woolhouse, M. E. J. et al. Heterogeneities in the transmission of infectious agents: Implications for the design of control programs 10.1073/pnas.94.1.338. 94, 338–342 (1997).

Used skills

Matrix modelling, programming in R, some data analysis.


Some experience in R would be useful. Interest in and knowledge of matrix calculus (Mathematics 3 level) is a prerequisite.

Other people involved in the supervision

Depending on the type of thesis, the data needed and the study program of the student, a second supervisor from a biological group may be required/advisable. Within the Biometris group, ample expertise in matrix modelling, theoretical ecology and statistical analysis is present.


At the moment the work should probably be conducted remotely (online).