Mathematical Epidemiology


The research activity of the group coordinated by Andrea Pugliese, currently including dr. Rachele Nieri (fixed-term researcher) and dr. Sara Sottile (post-doc) has been almost entirely devoted to the formulation and analysis of mathematical models in epidemiology and ecology.

Main research topics

Dynamics of vector-borne infections

Several infectious diseases are transmitted by vectors, among which mosquitoes and ticks. The dynamics of the infections thus depends on the population dynamics of the vectors and, for some infections, of non-human hosts. We have been studying for several years, in collaboration with the Italian institutes responsible for animal infections (Istituto Zooprofilattico Sperimentale di Lombardia ed Emilia-Romagna, e delle Venezie) the infection from West Nile Virus (WNV); it is mainly transmitted in a cycle between the common mosquitoes (Culex spp.) and several species of birds, but can be occasionally transmitted to humans and other mammals. Through the analysis of 10 years of data from Emilia-Romagna, we have identified that spring temperature is an important factor in determining the intensity of infections in a year; we are now working at understanding the role of bird immunity and other environmental and ecological factors in determining the infection dynamics, also with the aim of contributing to predictive models. We are also collaborating in the development of a computational model predicting Aedes mosquito abundance on a global scale, and the consequent potential risk of transmission of arboviruses (dengue, Zika and Chikungunya). In the past we have collaborated with Fondazione Edmund Mach (FEM) in the analysis of models for tick-borne infections, such as borreliosis and TBE.

Analysis of immuno-epidemiological models

In immuno-epidemiological models between-host transmission dynamics is coupled to intra-host immunological interactions; the immunological system is very complex, but, if a within-host model is only an ingredient of a multi-scale epidemic model, it is customary to resort to very simple model, in which the immune system is represented as a 1-d or 2-d variable. Despite the lack of details, this type of models has given relevant insights in understanding likely evolutionary outcomes, and shown potential epidemic dynamics that extend what expected from simple epidemic models. We are now particularly focusing on models allowing for partial and waning immunity, both in a complete immuno-epidemiological and in simpler epidemic models, inspired to the more complex model.

Behavioural Epidemiology of Infectious Diseases

Individuals can change their social behaviour spontaneously in response to an epidemic, e.g. during vaccination campaigns. In the age of social media these opinion dynamics are facilitated by the modern communication technologies, causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases. The aim of BEID is the inclusion in epidemic models of the description of human decision making (concerning, e.g., vaccination choices, social distancing, mobility patterns). We have analysed an SIR epidemic model coupled with an evolutionary vaccination game embedding the public health system efforts to increase vaccine uptake, assuming that the switching to the strategy “pro vaccine” depends on the incidence of the disease. A natural extension can include a time-delay in the information variables, depending on the previous information. A related ongoing project concerns a coupled info-epidemic system for misinformation and virus spreading.

Epidemics on complex structures

Most classical epidemic models assume that all individuals mix homogeneously. It is clear that such an assumption is far from reality, and different models have been proposed in which such an assumption is relaxed. We have considered a deterministic SAIRS epidemic model (with asymptomatic and symptomatic infections) in a multi-group setting (i.e., it is assumed that homogeneous mixing occurs within each group, while a matrix describes infectious contacts between subpopulations), obtaining conditions for the global asymptotic stability of the endemic equilibrium. In the limit when the number of groups is very large, but each has a small size, one obtains the (stochastic) epidemic models in households; in this case, we have been exploring what is the effect on the overall epidemic dynamics of sudden changes in contact rates in one only of the settings, mimicking the effect of lock-downs or other restrictions of contacts. Another type of modelling involves contact networks in which infections occur only when a susceptible and an infected individual are connected through a link; in this setting, we have both analysed simulations of synthetic networks, and studied the behaviour of deterministic models obtained through the so-called pair approximation.

Use of methods from singular perturbation theory in the analysis of epidemic models.

In models for endemic infectious diseases there is a natural difference in time-scales between the infection period and the period of susceptible recruitment by new births or immunity loss. The systems are not in the standard form of singular perturbation theory with slow and fast equations, but it is still possible to divide the flow into slow and fast parts, and to use the entry-exit map to characterize the exit from the fast flow. We have used this idea to analyse several models in the literature, from the SIRS and SIR model with demography to an SIRS epidemic model in which a network structure is considered through pair approximation, to models including immunity waning and boosting, and finally to the model discussed above in behavioural epidemiology. While f the dynamics of the SIR and SIR models was already well known, and the method has simply helped in giving more details on the dynamics in the transient phase, in the other cases the use of Geometrical Singular Perturbation Theory (GSPT) has provided new insights in the system’s behaviour. We plan to extend the use of the method to other epidemic models, considering also models with non-exponential infection and immunity periods.

Health Technology Assessment of vaccination strategies

We have been involved in cost-effectiveness studies evaluating the potential effect of introducing a vaccine in a population, or of substituting a new vaccine to the one(s) currently used. In particular, we have participated in the evaluation of the introduction of a live attenuated influenza vaccine in the Italian pediatric population: in the evaluation of the substitution of an adjuvanted influenza vaccine to the current vaccine in the elderly population in Spain; in the evaluation of the substitution of the pneumococcal vaccine PCV13 with PCV13 in the Italian pediatric population. These studies, that can be considered as translational research and were performed in collaboration with several public health experts and with support from vaccine producers, are based on an age-structured model of the infectious disease spread parameterised to available data, and simulate the effect of the new vaccine on the basis of existing studies on vaccine effectiveness. The results are then presented, in terms of costs and benefits for the sanitary system and for the society, both as expected average effect and possible distribution due to all uncertainties.

Modelling and control of insect pests

We have an on-going collaboration with the FEM and with the Center C3A of the University on this topic. In the past years, we collaborated on a model of biological control of the fruit fly Drosophila suzukii using augmentative releases of local parasitoids, such as Leptopilina japonica. Recently, the Ministero dell’agricoltura, della sovranità alimentare e delle foreste approved the introduction and release of the specialist parasitoid Ganaspis brasiliensis in Italy and we are planning to update the study considering releases of this larval parasitoid. An ongoing project concerns the potential use of vibrations for controlling the leafhopper Scaphoideus titanus, vector of the flavescence dorée pathogen in grapevine. Behavioral manipulation techniques consist in interfering with the communication of the pest in order to disrupt noxious behavior, such as mating and feeding. Even though the use of chemicals is widely used for this purpose, only in recent years, substrate-borne vibrations strategies have been implemented in the emerging field of applied biotremology. Models can help in understanding the mechanisms of action and support the decision of growers. Finally, we have started contacts with the Department of Public Health of the University La Sapienza and with the Foundation Bruno Kessler on modelling the releases of Wolbachia infected Aedes albopictus mosquitoes as a technique to reduce the size of mosquito populations.


Dynamics of vector-borne infections:
Zooprofilattico Sperimentale di Lombardia ed Emilia-Romagna:
Analysis of immuno-epidemiological models:
Behavioural Epidemiology of Infectious Diseases:
Epidemics on complex structures:
Use of singular perturbation methods in epidemic models:
Health Technology Assessment of vaccination strategies:
Modelling and control of insect pests:

Thesis proposal

We are available for offering Master’s or PhD thesis on any of the areas illustrated above. If interested, please contact Prof. Pugliese for agreeing on a possible topic for a thesis.