Age-selective harvesting in a delayed predator–prey model with fear effect.

(iii) The interaction between prey and predator is of Holling type-II functional response: HT <math display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mtable class="align" columnalign="left"><mtr><mtd columnalign="right"><mfrac><mi mathvariant="normal">d</mi><mi>X</mi><mi mathvariant="normal">d</mi><mi>t</mi></mfrac></mtd><mtd columnalign="left"><mo>=</mo><mfrac><msub><mi>b</mi><mn>1</mn></msub><mi>X</mi><mn>1</mn><mo>+</mo><mi>K</mi><mi>Y</mi></mfrac><mo>-</mo><msub><mi>d</mi><mn>1</mn></msub><mi>X</mi><mo>-</mo><msub><mi> </mi><mn>1</mn></msub><msup><mi>X</mi><mn>2</mn></msup><mo>-</mo><mfrac><mi> </mi><mi>X</mi><mi>Y</mi><mrow><msub><mi>b</mi><mn>2</mn></msub><mo>+</mo><mi>X</mi></mrow></mfrac></mtd></mtr><mtr><mtd columnalign="right"><mfrac><mi mathvariant="normal">d</mi><mi>Y</mi><mi mathvariant="normal">d</mi><mi>t</mi></mfrac></mtd><mtd columnalign="left"><mo>=</mo><mfrac><mrow><msub><mi>a</mi><mn>1</mn></msub><mi> </mi><mi>X</mi><mi>Y</mi></mrow><mrow><msub><mi>b</mi><mn>2</mn></msub><mo>+</mo><mi>X</mi></mrow></mfrac><mo>-</mo><msub><mi> </mi><mn>2</mn></msub><mi>Y</mi><mo>.</mo></mtd></mtr></mtable></math> ht Graph (2.7) Here, 2 and represent natural death rate and coefficient of consumption rate, respectively, of the predator population, b 2 is the half saturation constant, a 1 denotes the conversion factor. So, the decline rate is given by HT <math overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msub><mi>N</mi><mn>1</mn></msub><mo>+</mo><mi> </mi><msubsup><mi>N</mi><mn>1</mn><mn>2</mn></msubsup></math> ht and the growth rate is I bN i SB 1 sb , both depend on the present population size. [Extracted from the article]