Persistence and extinction of infection in stochastic population model with horizontal and imperfect vertical disease transmissions

Abhijit Majumder; Debadatta Adak; Adeline Samson; Nandadulal Bairagi; Abhijit Majumder; Debadatta Adak; Adeline Samson; Nandadulal Bairagi

doi:10.3934/mbe.2025030

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 4: 846-875. doi: 10.3934/mbe.2025030

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Persistence and extinction of infection in stochastic population model with horizontal and imperfect vertical disease transmissions

1.
Department of Biological Sciences and Eck Institute for Global Health, University of Notre Dame, Notre Dame, IN 46556, USA
2.
Department of Mathematics, Maharaja Bir Bikram University, Agartala 799004, India
3.
Laboratoire Jean Kuntzmann, University of Grenoble Alpes, Grenoble 38000, France
4.
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

Received: 11 August 2024 Revised: 20 December 2024 Accepted: 10 February 2025 Published: 05 March 2025

Epidemic models are used to understand the dynamics of disease transmission and explore the possible measures for preventing the spread of infection in the population. Disease transmission is intrinsically random and severely affected by environmental factors. We investigated a stochastic population model of the susceptible-infected-susceptible (SIS) type, in which infection spreads via both vertical and horizontal transmission routes. To incorporate stochasticity to the system, white multiplicative noise was taken into account in the horizontal disease transmission term. We proved that noise intensity, disease transmission, and recovery rates are potential routes for eradicating the disease. Furthermore, the parasite population reduces its fitness for some fixed noise if the relative fecundity of infected hosts and the disease transmission are low. However, if either of these is increased, it observes enhanced fitness. A simulation study illustrated the system's analytically dynamic properties and provided different insights. A case study for the imperfect vertical and horizontal infection transmission is also presented, supporting some of our observed theoretical results.
- stochastic population model,
- environmental factors,
- perfect and imperfect vertical transmissions,
- disease extinction time,
- persistence,
- stationary distribution,
- relative fecundity
Citation: Abhijit Majumder, Debadatta Adak, Adeline Samson, Nandadulal Bairagi. Persistence and extinction of infection in stochastic population model with horizontal and imperfect vertical disease transmissions[J]. Mathematical Biosciences and Engineering, 2025, 22(4): 846-875. doi: 10.3934/mbe.2025030

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Abstract

Epidemic models are used to understand the dynamics of disease transmission and explore the possible measures for preventing the spread of infection in the population. Disease transmission is intrinsically random and severely affected by environmental factors. We investigated a stochastic population model of the susceptible-infected-susceptible (SIS) type, in which infection spreads via both vertical and horizontal transmission routes. To incorporate stochasticity to the system, white multiplicative noise was taken into account in the horizontal disease transmission term. We proved that noise intensity, disease transmission, and recovery rates are potential routes for eradicating the disease. Furthermore, the parasite population reduces its fitness for some fixed noise if the relative fecundity of infected hosts and the disease transmission are low. However, if either of these is increased, it observes enhanced fitness. A simulation study illustrated the system's analytically dynamic properties and provided different insights. A case study for the imperfect vertical and horizontal infection transmission is also presented, supporting some of our observed theoretical results.

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