Bruno Buonomo

Università degli Studi di Napoli "Federico II", Mathematics and Applications, Faculty Member

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POSITION
Full professor, University of Naples Federico II

EDUCATION
Degree in Mathematics, University of Naples Federico II
PhD in Mathematics, University of Naples Federico II

VISITING/TEACHING
University of Glasgow, 1999/2000
University of Basilicata, 2003/2005
Xi'an Jiaotong University, Xi'an, China, 2004
Southwest Normal University, Chongqing, China, 2008
University of Gulu Uganda, 2009
Universidad Autonoma de Yucatan (UADY), Mexico, 2012
Universidad Nacional Autonoma de Mexico (UNAM), 2012
Fudan University, Shanghai, China, 2012

TEACHING AT FEDERICO II
Evolutionary Processes in Mathematical Physics
Mathematical Physics
Statistics

FIELD OF INTEREST
Analysis and control of evolution equations, in finite and infinite dimensional spaces, mainly concerning with Biomathematics

PAST AND PRESENT COLLABORATIONS
Eric Avila Vales (UADY, Yucatan, Mexico)
Andrea Di Liddo (National Research Council, Bari)
Alberto d'Onofrio (IPRI, Lyon, France)
Paolo Fergola (University of Naples Federico II)
Vincent Hull (Central Hydrobiology Laboratory, Rome)
Deborah Lacitignola (University of Cassino)
Salvatore Rionero (University of Naples Federico II)
Cruz Vargas De-Leon (University of Guerrero, Mexico)
Supervisors: Paolo Fergola (Naples Federico II, Master thesis) and Salvatore Rionero (Naples Federico II, PhD thesis)
Phone: +39.081.675630
Address: Dep. Mathematics and Applications
University of Naples Federico II
via Cintia,
80126 NAPLES
ITALY

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Andrej Dujella

University of Zagreb

Oleg Yu Vorobyev

Siberian Federal University

Asep K Supriatna

University of Padjadjaran (UNPAD)

Nicolae Radu Zabet

University of Essex

Jeffrey Townsend

Yale University

Muhammad Waziri

University of Maiduguri

Samit Chakrabarty

University of Leeds

Fabio Cuzzolin

Oxford Brookes University

Ghader Rezazadeh

Urmia University

Mikail F Lumentut

National Taiwan University

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Papers by Bruno Buonomo

The effect of time delay in plant-pathogen interactions with host demography

Mathematical Biosciences and Engineering,12, n.3, 473-490 (2015)

Modeling human response to bed–net promotion campaigns and its impact on malaria transmission

Advances in Applied Mathematics (A. R. Ansari ed.), Springer Proceedings in Mathematics and Statistics 87, pp. 23-30, Springer, 2014

We consider a malaria model including human response to health-promotion campaign for bed-net usa... more We consider a malaria model including human response to health-promotion campaign for bed-net usage. We propose a formulation of the human-mosquito contact rate which is based on the idea of information-dependent epidemic
models. We show that the model allows to easily determine optimal control strategies for implementing health campaigns. Moreover, the controlled system may predict a dramatic reduction of malaria incidence even when the uncontrolled
system predicts stable endemicity.

Qualitative analysis and optimal control of an epidemic model with vaccination and treatment

Mathematics and Computers in Simulation,100, 88-102 (2014)

"We focus on an epidemic model which incorporates a non-linear force of infection and two control... more "We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control.
The case of time–dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the
qualitative analysis provide a rather complete picture of the possible outcomes of the model."

A note on the direction of the transcritical bifurcation in epidemic models

Nonlinear Analysis: Modelling and Control, 20, n. 1, 38-55 (2015)

In classical epidemic models, it is common to observe that a disease-free equilibrium looses it... more In classical epidemic models, it is common to observe that a disease-free equilibrium
looses its stability for Ro = 1 and a transcritical bifurcation takes place. We analyze this aspect
from the point of view of the mathematical structure of models, in order to assess which parts
of the structure might be responsible of the direction of the transcritical bifurcation. We formulate
a general criterion, which gives sufficient (resp. necessary) conditions for the occurrence of forward
(resp. backward) bifurcations. The criterion, obtained as consequence of a well known analysis of
the centre manifold for general epidemic models, is applied to several epidemic models taken from
the literature.

Stability and bifurcation in plant-pathogens interactions

Applied Mathematics and Computation, 232, 858–871 (2014)

We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshol... more We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory–inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.

Effects of mosquitoes host choice on optimal intervention strategies for malaria control

Acta Applicandae Mathematicae, 132, 127–138 (2014)

Modeling peer influence effects on the spread of high-risk alcohol consumption behavior

Ricerche di Matematica, 63, n. 1, 101-117 (2014)

Modeling of pseudo-rational exemption to vaccination for SEIR diseases

Journal of Mathematical Analysis and Applications, 404, n. 2, 385-398 (2013)

Stability and bifurcation analysis of a vector-bias model of malaria transmission

Mathematical Biosciences, 242, n.1, 59-67 (2013)

The vector-bias model of malaria transmission, recently proposed by Chamchod and Britton, is cons... more The vector-bias model of malaria transmission, recently proposed by Chamchod and Britton, is considered. Nonlinear stability analysis is performed by means of the Lyapunov theory and the LaSalle Invariance Principle. The classical threshold for the basic reproductive number, R0, is obtained: if R0 > 1, then the disease will spread and persist within its host population. If R0 < 1, then the disease will die out. Then, the model has been extended to incorporate both immigration and disease-induced death of
humans. This modification has been shown to strongly affect the system dynamics. In particular, by using the theory of center manifold, the occurrence of a backward bifurcation at R0 = 1 is shown possible. This implies that a stable endemic equilibrium may also exists for R0 < 1. When R0 > 1, the endemic persistence
of the disease has been proved to hold also for the extended model. This last result is obtained by means of the geometric approach to global stability.

Modelling the influence of public's memory on the corruption-popularity dilemma in politics

Journal of Optimization Theory and Applications, 158 (2), 554-575 (2013)

We consider the problem of a rational politician who gains benefit from both being popular and co... more We consider the problem of a rational politician who gains benefit from both being popular and corrupt. In 1994, Feichtinger and Wirl studied this trade-off by means of an infinite-horizon optimal control approach. We reconsider the problem over a finite time-horizon, to model the dilemma of a politician who stays in office for a limited period of time and wishes to be reelected. We also include explicitly the possibility that awareness of politician's conduct to the general population is delayed and the effect of such delay on the politician's optimal behavior is analyzed. We show the outcomes under several different scenarios, with particular reference to the role of the politician's communication skills. One general conclusion is that the synergy of a good public's memory and immediate knowledge of corruption may often help the people to protect themselves from political corruption. Moreover, this synergy may greatly enhance the popularity of a politician with poor communication skills provided that he/she aims at maximizing benefit from popularity during his/her mandate.

$Figure 7: Influence of poor communication skills (k = 0.33) on political corruption (a) and popularity (b), for distinct values of 6 and delay kernel (Dotted line: weak kernel and 6 = 0.1. Dot-dashed line: weak kernel and 6 = 1. Solid line: strong kernel and 6 = 0.1. Dashed line: strong kernel and 6 = 1.). Here y = 0.2, 8 = 0, r = 0.1 and C\(0) = 0. The other parameter values are given in Table 1.$

$Figure 8: Influence of good communication skills (k = 2) on political corruption (a) and Popularity (b) for distinct values of 6 and delay kernel (Dotted line: weak kernel and 6 = 0.1. Dot-dashed line: weak kernel and 6 = 1. Solid line: strong kernel and 6 = 0.1. Dashed line: strong kernel and 6 = 1). Here y = 0.2, 6 = 0, r = 0.1 and C\(0) = 0. The other parameter values are given in Table 1.$

$Figure 10: Impact of large 8 (3 = 6.6), in case of poor communication skills (k = 0.33) of the politician, on political corruption (a) and Popularity (b) for distinct values of 6 and delay kernel (Dotted line: weak kernel and 6 = 0.1. Dot-dashed line: weak kernel and 6 = 1. Solid line: strong kernel and 6 = 0.1. Dashed line: strong kernel and 6 = 1). Here y = 0.2, r = 0.1 and C\(0) = 0. The other parameter values are given in Table 1.$

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The geometric approach to global stability in behavioral epidemiology

In: Modeling the Interplay between Human Behavior and Spread of Infectious Diseases (P. Manfredi and A. d'Onofrio eds), pp. 289-309, Springer, 2013

Three behavioral-epidemic models (i.e. epidemic systems including feedbacks that the information ... more Three behavioral-epidemic models (i.e. epidemic systems including feedbacks that the information about an infectious disease has on its spreading) are introduced. Two relevant feedbacks are explicitly considered: the pseudo-rational exemption to vaccination and the information--related changes in contact patterns by healthy subjects.
The global stability analysis of the endemic states is performed by means of the geometric approach to stability, with particular focus on a model of vaccination of adult susceptible subjects. Biological implications of the results are discussed.

Forces of infection allowing for backward bifurcation in an epidemic model with vaccination and treatment

Acta Applicandae Mathematicae, 122, n. 1, 283-293 (2012)

We consider an epidemic model for the dynamics of a vaccine-preventable disease, which incorporat... more We consider an epidemic model for the dynamics of a vaccine-preventable disease, which incorporates the treatment and an imperfect vaccine given to susceptible individuals. We show that in spite of the simple structure of the model, a backward bifurcation may always occur (depending on the treatment) when the force of infection is represented by any functional which is infinitesimal of the same order of the size of the infectious compartment, I, as I approaches zero. This includes many commonly used functionals, as the linear, the monotone saturating Michaelis-Menten and the non-monotone force of infection used to represent the "psychological effect".

Globally stable endemicity for infectious diseases with information-related changes in contact patterns

Applied Mathematics Letters, 25, n. 7, 1056-1060 (2012)

SIR and SIS epidemic models with information—related changes in contact patterns are introduced. ... more

Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: a theoretical study

by Bruno Buonomo and Eleonora Messina

Mathematical Biosciences and Engineering, 9, n.3, 539-552 (2012)

When a newly emerging human infectious disease spreads through a host population, it may be that ... more When a newly emerging human infectious disease spreads through a host population, it may be that public health authorities must begin facing the outbreaks and planning an intervention campaign when not all intervention tools are readily available. In such cases, the problem of finding optimal intervention strategies to minimize both the disease burden and the intervention costs may be addressed by considering multiple intervention regimes. In this paper, we consider the scenario in which authorities may rely initially only on non-pharmaceutical interventions at the beginning of the campaign, knowing that a vaccine will later be available, at an exogenous and known switching time. We use a two-stage optimal control problem over a finite time horizon to analyze the optimal intervention strategies during the whole campaign, and to assess the effects of the new intervention tool on the preceding stage of the campaign. We obtain the optimality systems of two connected optimal control problems, and show the solution profiles through numerical simulations.

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Global stability for an HIV-1 infection model including an eclipse stage of infected cells

Journal of Mathematical Analysis and Applications, 385, n.2, 709-720 (2012)

We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (J. ... more We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (J. Theoret. Biol. 247, 2007). One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. In Rong et al., the stability of the infected equilibrium has been analyzed locally. Here, we perform the global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on the higher-order generalization of Bendixson’s criterion. We obtain sufficient conditions written in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.

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On the optimal vaccination strategies for horizontally and vertically transmitted infectious diseases

Journal of Biological Systems, 19, n.2, 263-279 (2011)

We consider an SEIR epidemic model for an infectious disease that spreads in the human host popul... more We consider an SEIR epidemic model for an infectious disease that spreads in the human host population through both horizontal and vertical transmission. A periodically varying contact rate is introduced to simulate recurrent outbreaks.We use the optimal control theory to assess the disease control. Optimal vaccination strategies to minimize both the disease burden and the intervention costs are analyzed. We derive the optimality system and solve it numerically. The theoretical findings are then used to simulate a vaccination campaign for rubella under several scenarios, by using epidemiological parameters obtained by real data

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On the backward bifurcation of a vaccination model with nonlinear incidence

Nonlinear Analysis: Modelling and Control, 16, n.1: 30-46 (2011)

A compartmental epidemic model, introduced by Gumel and Moghadas (App. Math. Comput., 143, 2003),... more A compartmental epidemic model, introduced by Gumel and Moghadas (App. Math. Comput., 143, 2003), is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced by Castillo-Chavez and Song, (Math. Biosci. Eng., 1, 2004), which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective.

A simple analysis of vaccination strategies for rubella.

Mathematical Biosciences and Engineering, 8, n.3: 677-687 (2011)

We consider an SEIR epidemic model with vertical transmission introduced by Li, Smith and Wang (S... more We consider an SEIR epidemic model with vertical transmission introduced by Li, Smith and Wang (SIAM J. Appl. Math., 62, 2001), and apply optimal control theory to assess the effects of vaccination strategies on the model dynamics. The strategy is chosen to minimize the total number of infectious individuals and the cost associated with vaccination. We derive the optimality system and solve it numerically. The theoretical findings are then used to simulate a vaccination campaign for rubella in China.

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On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate

Applied Mathematics and Computation, 217, n.8: 4010-4016 (2010)

"We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incid... more "We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be a general nonlinear function of the susceptibles and the
infectious classes. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability are also obtained. Unlike the recent literature on this subject, here no restrictions are required about the monotonicity and concavity of the incidence rate with respect to the infectious class. Among the applications, the noteworthy case of a convex
incidence rate is provided."

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Analysis of a tuberculosis model with a case study in Uganda

Journal of Biological Dynamics, 4, n. 6, 571-593 (2010)

We consider a four-compartment tuberculosis model including exogenous reinfection.We derive suffi... more We consider a four-compartment tuberculosis model including exogenous reinfection.We derive sufficient conditions, in terms of the parameters of the system, which guarantee the occurrence of backward bifurcation. We also discuss the global stability of the endemic state by using a generalization of the Poincaré–Bendixson criterion.An application is given for the case of Internally Displaced People’s Camps in North Uganda. The study suggests how important it is to provide qualitative indications on the threshold value of the population density in the area occupied by the camps, in order to possibly eradicate the disease.

The effect of time delay in plant-pathogen interactions with host demography

Mathematical Biosciences and Engineering,12, n.3, 473-490 (2015)

Modeling human response to bed–net promotion campaigns and its impact on malaria transmission

Advances in Applied Mathematics (A. R. Ansari ed.), Springer Proceedings in Mathematics and Statistics 87, pp. 23-30, Springer, 2014

Qualitative analysis and optimal control of an epidemic model with vaccination and treatment

Mathematics and Computers in Simulation,100, 88-102 (2014)

A note on the direction of the transcritical bifurcation in epidemic models

Nonlinear Analysis: Modelling and Control, 20, n. 1, 38-55 (2015)

Stability and bifurcation in plant-pathogens interactions

Applied Mathematics and Computation, 232, 858–871 (2014)

Effects of mosquitoes host choice on optimal intervention strategies for malaria control

Acta Applicandae Mathematicae, 132, 127–138 (2014)

Modeling peer influence effects on the spread of high-risk alcohol consumption behavior

Ricerche di Matematica, 63, n. 1, 101-117 (2014)

Modeling of pseudo-rational exemption to vaccination for SEIR diseases

Journal of Mathematical Analysis and Applications, 404, n. 2, 385-398 (2013)

Stability and bifurcation analysis of a vector-bias model of malaria transmission

Mathematical Biosciences, 242, n.1, 59-67 (2013)

Modelling the influence of public's memory on the corruption-popularity dilemma in politics

Journal of Optimization Theory and Applications, 158 (2), 554-575 (2013)

Download

The geometric approach to global stability in behavioral epidemiology

In: Modeling the Interplay between Human Behavior and Spread of Infectious Diseases (P. Manfredi and A. d'Onofrio eds), pp. 289-309, Springer, 2013

Forces of infection allowing for backward bifurcation in an epidemic model with vaccination and treatment

Acta Applicandae Mathematicae, 122, n. 1, 283-293 (2012)

Globally stable endemicity for infectious diseases with information-related changes in contact patterns

Applied Mathematics Letters, 25, n. 7, 1056-1060 (2012)

SIR and SIS epidemic models with information—related changes in contact patterns are introduced. ... more

Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: a theoretical study

by Bruno Buonomo and Eleonora Messina

Mathematical Biosciences and Engineering, 9, n.3, 539-552 (2012)

Download

Global stability for an HIV-1 infection model including an eclipse stage of infected cells

Journal of Mathematical Analysis and Applications, 385, n.2, 709-720 (2012)

Download

On the optimal vaccination strategies for horizontally and vertically transmitted infectious diseases

Journal of Biological Systems, 19, n.2, 263-279 (2011)

Download

On the backward bifurcation of a vaccination model with nonlinear incidence

Nonlinear Analysis: Modelling and Control, 16, n.1: 30-46 (2011)

A simple analysis of vaccination strategies for rubella.

Mathematical Biosciences and Engineering, 8, n.3: 677-687 (2011)

Download

On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate

Applied Mathematics and Computation, 217, n.8: 4010-4016 (2010)

Download

Analysis of a tuberculosis model with a case study in Uganda

Journal of Biological Dynamics, 4, n. 6, 571-593 (2010)

Influence of information-driven human behavior on the spread and control of infectious diseases

Invasive species and related infectious diseases: modelling and control

Modeling the impact of human behavior on the spread of mosquito-borne diseases

Vector-bias in malaria models

Modelling the effect of mosquitoes host choice on malaria transmission

Some remarks on transcritical bifurcations in epidemic models

Modeling the optimal use of intervention tools to control epidemic disease outbreaks

Mechanisms leading to backward bifurcation in epidemic models

The geometric approach to global stability in behavioural epidemiology

Mathematical approaches to infectious diseases control

Nonlinear stability of epidemic models including information-related human behaviour

Optimal vaccination strategies for vertically transmitted diseases

Pricing and advertising strategies in fashion markets

Global stability for a four dimensional epidemic model

On some aspects concerning the geometric approach to stability

On the Lyapunov stability for SIRS epidemic models with nonlinear incidence rate

Bruno Buonomo

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