Table 2 The determined optimal ARFIMA for different zoonotic and vector-borne diseases

ARFIMA (2,0.462,1) (1,0.379,1)₁₂ for HFRS incidence series between January 2004 and July 2023

AR1

0.752

0.138

5.459

 < 0.001

2574.856

2609.451

− 1277.43

0.004

0.951

AR2

− 0.397

0.076

− 5.197

 < 0.001

MA1

0.285

0.152

1.875

0.031

SAR1

0.966

0.04

24.204

 < 0.001

SMA1

0.929

0.079

11.818

 < 0.001

Pulse change

− 82.137

138.167

− 0.594

0.552

ARFIMA (1,0,1) (1,0.06,2)₁₂ for rabies incidence series between January 2004 and July 2023

AR1

0.941

0.024

38.618

 < 0.001

1518.222

1552.818

− 749.111

0.662

0.416

MA1

0.417

0.085

4.916

 < 0.001

SAR1

0.914

0.064

14.309

 < 0.001

SMA1

0.649

0.207

3.135

0.002

SMA2

− 0.163

0.079

− 2.075

0.038

Pulse change

− 2.038

15.773

− 0.129

0.897

ARFIMA (0,0,1) (0,0.072,0)₁₂ for dengue fever incidence series between January 2004 and July 2023

MA1

− 0.59

0.049

− 11.923

 < 0.001

3547.62

3568.38

− 1767.81

0.705

0.401

Pulse change

− 467.039

542.679

− 0.861

0.389

ARFIMA (1,-0.732,(1,2,3,4,6) (1,0.436,1)₁₂ for HB incidence series between January 2004 and July 2023

AR1

0.993

0.011

90.681

 < 0.001

3037.48

3085.92

− 1504.74

0.009

0.926

MA1

− 0.651

0.103

− 6.301

 < 0.001

MA2

− 0.419

0.108

− 3.874

 < 0.001

MA3

− 0.399

0.086

− 4.66

 < 0.001

MA4

− 0.22

0.09

2.447

0.014

MA6

− 0.12

0.066

− 1.825

0.035

SAR1

− 0.828

0.347

− 2.386

0.017

SMA1

− 0.8

0.367

− 2.183

0.029

Pulse change

2190.13

579.051

3.783

 < 0.001

ARFIMA (0,0,2) (2,0.163,1)₁₂ for Leptospirosis incidence series between January 2004 and July 2023

MA1

− 0.398

0.068

− 5.901

 < 0.001

1830.26

1864.86

905.13

0.064

0.8

MA2

− 0.143

0.068

− 2.119

0.034

SAR1

0.688

0.135

5.10

 < 0.001

SAR2

0.224

0.11

2.034

0.022

SMA1

0.40

0.163

2.452

0.014

Pulse change

6.882

15.675

0.439

0.661

ARFIMA (2,− 0.713,0) (1,0.29,1)₁₂ for malaria incidence series between January 2004 and July 2023

MA1

1.654

0.188

8.785

 < 0.001

1430.06

1457.91

− 706.031

0.001

0.971

MA2

− 0.659

0.183

− 3.605

 < 0.001

SAR1

− 0.996

0.01

− 98.859

 < 0.001

SMA1

− 0.985

0.024

− 40.556

 < 0.001

Pulse change

− 83.131

70.378

− 1.181

0.238

ARFIMA (4,0,0) (1,0,0)₁₂ for Schistosomiasis incidence series between January 2004 and July 2023

AR1

1.069

0.06

17.678

 < 0.001

3693.18

3717.4

− 1839.59

0.152

0.696

AR2

− 0.419

0.066

− 6.359

 < 0.001

AR4

0.15

0.043

3.503

 < 0.001

SAR1

0.143

0.063

2.26

0.024

Pulse change

− 213.922

419.083

− 0.511

0.61