Publications
2024
Bonnard, B., Rouot. J., Silva C.J.
Geometric optimal control of the generalized Lotka–Volterra model of the intestinal microbiome,
Optim. Control Appl. Meth. 2024;1-31.
doi: 10.1002/oca.3089; https://hal.science/hal-03861565
Tedim, S., Afreixo, A., Felgueiras, M., Leitão, R.P., Pinheiro, S.J., Silva, C.J..
Evaluating COVID-19 in Portugal: Bootstrap confidence interval.
AIMS Mathematics, 2024, 9(2): 2756-2765.
https://doi.org/10.3934/math.2024136
2023
Zaitri, Mohamed A., Cristiana J. Silva, and Delfim F. M. Torres,
An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia,
Axioms 12, no. 9: 867, 2023.
https://doi.org/10.3390/axioms12090867
Martins, Natália, Ricardo Almeida, Cristiana J. Silva, and Moulay Rchid Sidi Ammi,
"Editorial for the Special Issue of Axioms “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday”, Axioms 12, no. 2: 110, 2023.
https://doi.org/10.3390/axioms12020110
Ghaffari, Peyman, Silva, Cristiana J., Torres, Delfim F. M.,
Mathematical models and optimal control in mosquito transmitted diseases,
In: Bio-mathematics, Statistics, and Nano-Technologies, New York, 2023.
doi: https://doi.org/10.1201/9781003035992
2022
Guillaume Cantin, Cristiana J. Silva,
Complex network near-synchronization for non-identical predator-prey systems.
AIMS Mathematics, 2022, 7(11): 19975-19997.
Guillaume Cantin, Cristiana J. Silva, Arnaud Banos,
Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic.
Networks and Heterogeneous Media, Vol. 17, No. 3, 2022, pp. 333-357.
Cristiana J. Silva,
Stability and optimal control of a delayed HIV/AIDS-PrEP model.
Discrete & Continuous Dynamical Systems - S, 2022, 15(3): 639-654.
Jorge Cabral, Vera Afreixo, Cristiana J Silva, Ana Tavares & Alda Marques,
A Multiobjective Optimization Approach to Pulmonary Rehabilitation Effectiveness in COPD.
In Statistics, Optimization & Information Computing, Vol. 11, Issue 2, pp. 299–331, 2022.
https://doi.org/10.19139/soic-2310-5070-1505
Pedro Machado, Sofia J. Pinheiro, Vera Afreixo, Cristiana J. Silva, and Rui Leitão,
Graph Theory Approach to COVID-19 Transmission by Municipalities and Age Groups,
Mathematical and Computational Applications 27, no. 5: 86, 2022.
https://doi.org/10.3390/mca27050086
Mohamed A. Zaitri, Cristiana J. Silva and Delfim F. M. Torres,
Stability Analysis of Delayed COVID-19 Models,
Axioms 2022, 11, 400.
https://doi.org/10.3390/axioms11080400
Ana P. Lemos-Paião, Helmut Maurer, Cristiana J. Silva and Delfim F. M. Torres,
A SIQRB delayed model for cholera and optimal control treatment,
Math. Model. Nat. Phenom. 17 (2022) 25
https://doi.org/10.1051/mmnp/2022027
Adelaide Freitas, Sara Escudeiro, Juliana Reis, and Cristiana J. Silva,
COVID-19’s Pandemic: A New Way Of Thinking Through Linear Combinations Of Proportions,
in Mathematical Analysis of Infectious Diseases, Elsevier, 2022.
Cristiana J. Silva, Guillaume Cantin, Carla Cruz, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos, Delfim F. M. Torres,
Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves,
J. Math. Anal. Appl. 514 (2022), no. 2, Art. 125171, 25 pp.
https://www.sciencedirect.com/science/article/pii/S0022247X2100250X
https://arxiv.org/abs/2010.02368
Loïc Michel, Cristiana J. Silva, Delfim F. M. Torres,
Model-free based control of a HIV/AIDS prevention model.
Mathematical Biosciences and Engineering, 2022, 19(1): 759--774.
doi: 10.3934/mbe.2022034
2021
Zita Abreu, Guillaume Cantin, Cristiana J. Silva,
Analysis of a COVID-19 compartmental model: a mathematical and computational approach,
Mathematical Biosciences and Engineering, 2021, 18(6): 7979-7998.
doi: 10.3934/mbe.2021396
Cristiana J. Silva, Carla Cruz, Delfim F. M. Torres, Alberto P. Munuzuri, Alejandro Carballosa, Ivan Area, Juan J. Nieto, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevao Soares dos Santos, Wilson Abreu, Jorge Mira,
Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal,
https://doi.org/10.1038/s41598-021-83075-6
Scientific Reports COVID-19 Collection: https://www.nature.com/collections/jjghbagfjg
https://arxiv.org/abs/2009.00660
R. Almeida, N. Martins, C. J. Silva,
Global stability condition for the disease-free equilibrium point of fractional epidemiological models,
Axioms, vol. 10 n.4, 2021, article-number 238.
URL: https://www.mdpi.com/2075-1680/10/4/238
F. Ndairou, I. Area, J. J. Nieto, C. J. Silva and D. F. M. Torres,
Fractional model of COVID-19 applied to Galicia, Spain and Portugal,
Chaos Solitons Fractals, Chaos Solitons Fractals 144 (2021), Art. 110652, 7 pp.
Preprint: http://arxiv.org/abs/2101.01287
URL: http://dx.doi.org/10.1016/j.chaos.2021.110652
Juliana Couras, Ivan Area, Juan J. Nieto, Cristiana J. Silva, Delfim F. M. Torres,
Optimal control of vaccination and plasma transfusion with potential usefulness for COVID-19,
In: 'Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact', Springer Nature Singapore Pte Ltd, 509-525 (2021).
https://doi.org/10.1007/978-981-16-2450-6_23
https://arxiv.org/abs/2010.04146
Cristiana J. Silva, G. Cantin,
Synchronization and Self-organization in Complex Networks for a Tuberculosis Model,
Math. Comput. Sci. 15 (2021), no. 1, 107--120.
https://doi.org/10.1007/s11786-020-00472-2
2020
Ana P. Lemos-Paião, Cristiana J. Silva and Delfim F. M. Torres,
A New Compartmental Epidemiological Model for COVID-19 with a Case Study of Portugal,
Ecological Complexity 44 (2020) Art. 100885, 8 pp
Preprint: https://arxiv.org/abs/2011.08741
DOI: https://doi.org/10.1016/j.ecocom.2020.100885
Cristiana J. Silva, Delfim F. M. Torres,
On SICA models for HIV transmission,
In: Hattaf K., Dutta H. (eds) Mathematical Modelling and Analysis of Infectious Diseases. Studies in Systems, Decision and Control, vol 302. Springer, Cham. (2020).
https://doi.org/10.1007/978-3-030-49896-2_6
https://arxiv.org/abs/2004.11903
A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres,
A Survey on Sufficient Optimality Conditions for Delayed Optimal Control Problems.
In: Hattaf K., Dutta H. (eds) Mathematical Modelling and Analysis of Infectious Diseases. Studies in Systems, Decision and Control, vol 302. Springer, Cham. (2020) .
https://doi.org/10.1007/978-3-030-49896-2_12
https://arxiv.org/abs/2004.10029
A. P. Lemos-Paião, C. J. Silva, D. F. M. Torres and E. Venturino,
Optimal Control of Aquatic Diseases: A Case Study of Yemen's Cholera Outbreak,
J. Optim. Theory Appl. 185 (2020), no. 3, 1008--1030.
https://doi.org/10.1007/s10957-020-01668-z
https://arxiv.org/abs/2004.07402
Cristiana J. Silva, Delfim F. M. Torres,
Errata to "Modeling and optimal control of HIV/AIDS prevention through PrEP", Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 1, 119–141,
Discrete Contin. Dyn. Syst. Ser. S 13 (2020), no. 5, 1619–1621.
https://doi.org/10.3934/dcdss.2020343
Carlos Campos, Cristiana J. Silva, Delfim F. M. Torres,
Numerical Optimal Control of HIV Transmission in Octave/MATLAB
Math. Comput. Appl. 25 (2020), no. 1, 20 pp
doi: 10.3390/mca25010001
https://arxiv.org/abs/1912.09510
Cristiana J. Silva, Helmut Maurer,
Optimal control of HIV treatment and immunotherapy combination with state and control delays,
Optim Control Appl Meth . 2020 ;41:537-554.
doi: https://doi.org/10.1002/oca.2558
2019
Guillaume Cantin, Cristiana J. Silva,
Influence of the topology on the dynamics of a complex network of HIV/AIDS epidemic models,
AIMS Mathematics, 2019, 4(4): 1145-1169.
doi: 10.3934/math.2019.4.1145.
https://www.aimspress.com/article/10.3934/math.2019.4.1145
https://arxiv.org/abs/1911.05508
Djordević, J., Silva, C.J.,
A stochastic analysis of the impact of fluctuations in the environment on pre-exposure prophylaxis for HIV infection,
Soft. Comput. 25, 6731–6743 (2021).
Published online: 17 December 2019
doi:10.1007/s00500-019-04611-1
E. M. Lotfi, M. Mahrouf, M. Maziane, C. J. Silva, D. F. M. Torres and N. Yousfi,
A minimal HIV-AIDS infection model with general incidence rate and application to Morocco data,
Stat. Optim. Inf. Comput. 7 (2019), no. 2, 588--603.
http://www.iapress.org/index.php/soic/article/view/soic.20190906
Ana P. Lemos-Paiao, Cristiana J. Silva, Delfim F. M. Torres,
A sufficient optimality condition for non-linear delayed optimal control problems,
Pure Appl. Funct. Anal. 4 (2019), no. 2, 345--361.
https://arxiv.org/abs/1804.06937
Delfim F. M. Torres, Ivan. Area, Cesar Silva, Cristiana J. Silva,
The Portuguese Meeting in Biomathematics,
Statistics, Optimization and Information Computing, 2019.
http://www.iapress.org/index.php/soic/article/view/soic.20190901
Cristiana J. Silva, Delfim F. M. Torres,
Stability of a fractional HIV/AIDS model,
Math. Comput. Simul. 164 (2019), 180-190.
DOI: 10.1016/j.matcom.2019.03.016
http://arxiv.org/abs/1903.02534
Ana P. Lemos-Paiao, Cristiana J. Silva, Delfim F. M. Torres,
A sufficient optimality condition for delayed state-linear optimal control problems,
Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 5, 2293-2313.
https://arxiv.org/abs/1901.04340
2018
Jasmina Djordjevic, Cristiana J. Silva, Delfim F. M. Torres,
A stochastic SICA epidemic model for HIV transmission,
Appl. Math. Lett. 84 (2018), 168--175.
https://arxiv.org/abs/1805.01425
F. Ndairou, I. Area, J. J. Nieto, C. J. Silva, D. F. M. Torres,
Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil,
Math Meth Appl Sci. (41) 2018, 8929-8941.
https://arxiv.org/abs/1711.05630
Ana P. Lemos-Paião, Cristiana J. Silva, Delfim F. M. Torres
A cholera mathematical model with vaccination and the biggest outbreak of world’s history
AIMS Mathematics 3 (2018), no. 4, 448--463. doi: 10.3934/Math.2018.4.448
http://www.aimspress.com/article/10.3934/Math.2018.4.448
W. Wojtak, C. J. Silva, D. F. M. Torres,
Uniform asymptotic stability of a fractional tuberculosis model,
Math. Model. Nat. Phenom. 13 (2018), no. 1, Art. 9, 10 pp.
https://arxiv.org/abs/1801.07059
D. Rocha, C. J. Silva and D. F. M. Torres,
Stability and Optimal Control of a Delayed HIV Model,
Math. Methods Appl. Sci. 41 (2018), no. 6, 2251--2260.
DOI: 10.1002/mma.4207
http://arxiv.org/abs/1609.07654
F. Rodrigues, C. J. Silva, D. F. M. Torres and H. Maurer,
Optimal control of a delayed HIV model,
Discrete Contin. Dyn. Syst. Ser. B 23 (2018), no. 1, 443--458.
http://arxiv.org/abs/1708.06451
C. J. Silva and D. F. M. Torres,
Global stability for a HIV/AIDS model,
Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67 (2018), no. 1, 93--101.
DO I: 10.1501/Commua1_0000000833
C. J. Silva and D. F. M. Torres,
Modeling and optimal control of HIV/AIDS prevention through PrEP,
Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S) 11 (2018), no. 1, 119-141.
https://arxiv.org/abs/1703.06446
R. Denysiuk, C. J. Silva, D. F. M. Torres,
Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem,
Comput. Appl. Math. 37 (2018), no. 2, 2112--2128.
https://arxiv.org/abs/1703.05458
I. Area, F. Ndairou, J. J. Nieto, C. J. Silva, D. F. M. Torres,
Ebola Model and Optimal Control with Vaccination Constraints,
J. Ind. Manag. Optim. 14 (2018), no. 2, 427--446.
https://arxiv.org/abs/1703.01368
E. M. Rocha, C. J. Silva and D. F. M. Torres,
The effect of immigrant communities coming from higher incidence tuberculosis regions to a host country,
Ric. Mat. 67 (2018), no. 1, 89--112.
https://arxiv.org/abs/1701.09157
2017
C. J. Silva, D. F. M. Torres and Ezio Venturino,
Optimal Spraying in Biological Control of Pests,
Math. Model. Nat. Phenom. 12 (2017), no. 3, 51--64.
https://arxiv.org/abs/1704.04073
C. J. Silva and D. F. M. Torres,
A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde,
Ecological Complexity 30 (2017) 70-75.
DOI: 10.1016/j.ecocom.2016.12.001
https://arxiv.org/abs/1612.00732v1
A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres,
An epidemic model for cholera with optimal control treatment,
J. Comput. Appl. Math. 318 (2017) 168--180.
DOI:10.1016/j.cam.2016.11.002
https://arxiv.org/abs/1611.02195
C. J. Silva, H. Maurer, D. F. M. Torres,
Optimal control of a tuberculosis model with state and control delays,
Math. Biosci. Eng. 14 (2017), no. 1, 321--337
http://arxiv.org/abs/1606.08721
2015
C. J. Silva and D. F. M. Torres,
A TB-HIV/AIDS coinfection model and optimal control treatment,
Discrete Contin. Dyn. Syst., vol. 35, no. 9, 4639-4663, 2015.
http://arxiv.org/abs/1501.03322
C. J. Silva, D. F. M. Torres,
Optimal Control of Tuberculosis: A Review,
J. P. Bourguignon, R. Jeltsch, A. Pinto and M. Viana, Dynamics, Games and Science, 701-722,
Springer, CIM Series in Mathematical Sciences, 2015.
http://arxiv.org/abs/1406.3456
R. Denysiuk, C. J. Silva and D. F. M. Torres,
Multiobjective approach to optimal control for a tuberculosis model,
Optim. Methods Softw., 30, 2015, 893-910.
DOI:10.1080/10556788.2014.994704
http://arxiv.org/abs/1412.0528
2014
P. Rodrigues, C. J. Silva and D. F. M. Torres,
Cost-effectiveness analysis of optimal control measures for tuberculosis,
Bull. Math. Bio. 76 (2014), no. 10, 2627-2645.
http://link.springer.com/article/10.1007/s11538-014-0028-6?no-access=true
C. J. Silva and D. F. M. Torres,
Modeling TB-HIV Syndemic and Treatment,
Journal of Applied Mathematics, vol. 2014, Article ID 248407, 14 pages, 2014.
doi:10.1155/2014/248407.
http://www.hindawi.com/journals/jam/2014/248407/
2013
C. J. Silva and D. F. M. Torres,
An optimal control approach to malaria prevention via insecticide-treated nets,
Conference Papers in Mathematics, vol. 2013, Article ID 658468, 8 pages, 2013.
http://www.hindawi.com/journals/cpis/2013/658468/
C. J. Silva and D. F. M. Torres,
Optimal control for a tuberculosis model with reinfection and post-exposure interventions,
Math. Biosci. 244 (2013), no. 2, 154--164.
DOI:10.1016/j.mbs.2013.05.005
http://dx.doi.org/10.1016/j.mbs.2013.05.005
2012
Cristiana J. Silva and Delfim F. M. Torres,
Optimal control strategies for tuberculosis treatment: a case study in Angola,
Numer. Algebra Control Optim. 2 (2012), no. 3, 601--617.
2010
C. Silva, E. Trélat, Asymptotic approach on conjugate points for minimal time bangbang
control problems, Systems and Control Letters, 59, 720-733 (2010).
doi:10.1016/j.sysconle.2010.08.008.
http://www.sciencedirect.com/science/article/pii/S0167691110001131
C. J. Silva, E. Trélat, Smooth regularization of bang-bang optimal control problems,
IEEE - Transactions on Automatic Control, No. 11, 2488-2499 (2010).
doi:10.1109/TAC.2010.2047742
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5445043
C. J. Silva, Conjugate points for minimal-time bang-bang optimal control problems,
Bol. Soc. Port. Mat. Special Issue, 153-157 (2010).
2009
Cristiana J. Silva, Delfim F. M. Torres, Emmanuel Trélat,
O Controlo Óptimo e as suas Múltiplas Aplicações, Bol. Soc. Port. Mat. No. 61 (2009), 11-37.
http://arxiv.org/abs/0903.4019
http://www.spm.pt/catalogo/item/75
2006
C. J. Silva, D. F. M. Torres, Absolute Extrema of Invariant Optimal Control Problems,
Communications in Applied Analysis, Vol. 10 (2006), no. 4, 503-516
http://arxiv.org/abs/math/0608381
C. J. Silva, D. F. M. Torres, Two-dimensional Newton's Problem of Minimal Resistance,
Control and Cybernetics, Vol. 35 (2006), No. 4., 965-975.
http://arxiv.org/abs/math/0607197
------------Proceedings-------------
2021
Adela Iutis, Wilson Abreu, Adelaide Freitas, Cristiana J Silva,
Are demographic, clinical and psychosocial factors and depression symptoms associated with dementia risk among patients with HIV in Portugal?,
Journal of Statistics on Health Decision 3 (1) (2021), 40-43.
https://proa.ua.pt/index.php/jshd/article/view/24826
2016
D. Rocha, C. J. Silva and D. F. M. Torres,
Stability and Optimal Control of a Delayed HIV Model,
Proceedings of the 16th International Conference on Computational and Mathematical
Methods in Science and Engineering (CMMSE-2016), Costa Ballena (Rota),
Cádiz, Spain, July 4-8, 2016, 1071--1075.
ISBN 978-84-608-6082-2
A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres,
An epidemic model for cholera with treatment through quarantine,
Proceedings of the 16th International Conference on Computational and Mathematical
Methods in Science and Engineering (CMMSE-2016), Costa Ballena (Rota),
Cádiz, Spain, July 4-8, 2016, 752--757.
ISBN 978-84-608-6082-2
2013
C. J. Silva and D. F. M. Torres,
An optimal control approach to malaria prevention via insecticide-treated nets,
Conference Papers in Mathematics, vol. 2013, Article ID 658468, 8 pages, 2013.
P. Rodrigues, C.J. Silva, D.F.M. Torres,
Optimal control strategies for reducing the number of active infected individuals with tuberculosis,
Proceedings of the SIAM Conference on Control and Its Applications (CT13),
San Diego, California, USA, July 8--10, 2013, pp. 44--50.
2012
Cristiana J. Silva and Delfim F.M. Torres,
Optimal control applied to tuberculosis models,
``The IEA-EEF European Congress of Epidemiology 2012: Epidemiology for a Fair and Healthy Society'',
Eur. J. Epidemiol. (2012) 27, S1--S197.
DOI 10.1007/s10654-012-9722-6
Cristiana J. Silva and Delfim F. M. Torres,
Optimal control of tuberculosis in Angola,
Electronic proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS),
Paper 160 (2012).
------------ PhD Thesis -----------
C. J. Silva, Regularization and Bang-bang Conjugate Times in Optimal Control,
PhD thesis (supervisors: Delfim Torres and Emmanuel Trélat), University of
Aveiro (25%) and University of Orléans (France) (75%), 2010.
Master Thesis
C. J. Silva, Abordagens do Cálculo das Variações e do Controlo Óptimo ao problema
de Newton de Resistência Mínima, Master thesis (supervisor: Delfim Torres),
University of Aveiro, 2005.