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Table 1 Input data and model output for the period 1979–2018: total human population NTOT in 106, annual human net migration NMIG in 104 per year, reported tick-borne encephalitis (TBE) cases NTBE, vaccination coverage VC, four-year average of log-transformed Scandinavian indices SI, beech fructification index 2 years prior Fyear−2 and annual sunshine duration in hours SD

From: Tick-borne encephalitis (TBE) cases are not random: explaining trend, low- and high-frequency oscillations based on the Austrian TBE time series

Year

NTOT

N MIG

NTBE

VC

SI

Fyear−2

SD

N

NGLM1

NGLM2

NGLM3

NGLM4

1979

7.546

-0.002

677

0.03

0.974

1

1447

698

436

652

645

634

1980

7.553

0.009

438

0.07

0.904

1

1444

471

437

526

531

512

1981

7.584

0.030

294

0.15

0.836

1

1392

346

440

411

419

385

1982

7.564

-0.023

612

0.22

0.801

1

1719

785

438

508

546

602

1983

7.560

-0.002

240

0.29

0.725

0

1583

338

437

380

305

318

1984

7.563

0.003

336

0.35

0.794

2

1401

517

438

432

473

439

1985

7.567

0.006

300

0.41

0.824

1

1522

508

438

454

474

469

1986

7.573

0.006

258

0.46

0.804

2

1555

478

439

435

473

478

1987

7.576

0.002

215

0.51

0.837

0

1371

439

439

480

368

349

1988

7.594

0.013

201

0.56

0.744

2

1451

457

441

370

411

386

1989

7.645

0.045

131

0.60

0.722

2

1732

328

447

302

331

357

1990

7.711

0.059

89

0.63

0.714

0

1692

241

455

283

220

237

1991

7.799

0.077

128

0.65

0.728

2

1679

366

465

274

296

305

1992

7.883

0.071

84

0.67

0.759

2

1623

255

475

314

338

338

1993

7.929

0.034

102

0.71

0.815

1

1539

352

481

449

471

453

1994

7.943

0.003

178

0.74

0.859

3

1612

685

483

591

660

640

1995

7.953

0.002

109

0.78

0.848

0

1601

495

484

582

457

477

1996

7.965

0.004

128

0.78

0.899

1

1504

582

485

648

675

650

1997

7.971

0.002

99

0.79

0.767

3

1722

471

486

494

573

577

1998

7.982

0.008

62

0.80

0.704

0

1438

310

487

416

343

318

1999

8.002

0.020

41

0.82

0.732

0

1626

228

490

419

340

348

2000

8.021

0.017

60

0.84

0.695

1

1546

375

492

395

442

414

2001

8.064

0.042

54

0.86

0.783

1

1514

386

498

425

452

421

2002

8.100

0.034

60

0.87

0.871

2

1533

462

502

546

588

566

2003

8.143

0.043

82

0.87

0.873

1

2014

631

508

534

552

681

2004

8.201

0.054

54

0.87

0.840

1

1589

415

516

478

498

482

2005

8.254

0.050

100

0.88

0.862

1

1743

833

523

526

547

576

2006

8.283

0.025

84

0.88

0.872

2

1771

700

526

627

688

743

2007

8.308

0.023

45

0.88

0.827

0

1692

375

530

580

462

487

2008

8.335

0.024

87

0.87

0.837

2

1635

669

533

597

666

661

2009

8.352

0.018

79

0.86

0.835

1

1686

564

536

622

674

682

2010

8.375

0.022

63

0.85

0.837

0

1538

420

539

616

492

476

2011

8.408

0.031

113

0.86

0.889

3

1847

807

544

664

741

785

2012

8.452

0.044

52

0.85

0.885

0

1674

347

550

625

484

503

2013

8.508

0.056

99

0.82

0.880

3

1508

550

558

593

656

569

2014

8.585

0.074

80

0.85

0.892

0

1621

533

569

571

436

433

2015

8.700

0.114

71

0.85

0.828

1

1743

473

586

417

431

428

2016

8.773

0.065

89

0.84

0.807

1

1607

556

597

542

589

543

2017

8.822

0.045

116

0.82

0.772

0

1596

644

604

577

478

451

2018

8.859

0.035

154

0.82

0.747

3

2015

856

610

586

708

768

  1. The hypothetical TBE cases without vaccination N were simulated by 4 versions (development steps) of a generalized linear model, where the predicted TBE cases are given by N GLM1, N GLM2, N GLM3 and N GLM4