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The impact of two independent gaussian white noises on the behavior of a stochastic epidemic model

Yavuz Mehmet, Boulaasair Lahcen, Bouzahir Hassane, Diop Mamadou Abdoul, Benaid Brahim

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 1

121-134

The aim of this paper is to investigate a stochastic SIS (Susceptible, Infected, Susceptible) epidemic model in which the disease transmission coefficient and the death rate are subject to random disturbances. Using the convergence theorem for local martingales and solving the Fokker-Planck equation associated with the one-dimensional stochastic differential equation, we demonstrate that the disease will almost surely persist in the mean. In the case of global asymptotic stability of the endemic equilibrium for a SIS deterministic epidemic model, we formulate suitable conditions guaranteeing that the stochastic SIS model has a unique ergodic stationary distribution. Furthermore, we deal with the exponential extinction of the disease. Finally, some numerical simulations are provided to illustrate the obtained analytical results.

Genus-level versus species-level extinction rates

Trammer J.

Acta Geologica Polonica

2016

Vol. 66, no. 3

261--265

The average extinction rates of index species per m. y. are computed by means of a count-of-biozones metric (Trammer 2014). These rates and the average extinction rates of genera belonging to biostratigraphically important groups, calculated according to three different methods, show congruent rises and falls from the Cambrian to the Neogene. The extinction rates of genera are, thus, a relatively good predictor of species extinction rates.

Continuous versus pulsed origination and extinction and biozones

Trammer J.

Acta Geologica Polonica

2014

Vol. 64, no. 4

361--366

The count of biozones as an approximate measure of the origination and extinction rates of index taxa (mostly species) is proposed. The mean number of extinctions of these taxa per m.y. is 1.136 (Palaeozoic mean 0.902, Mesozoic mean 1.680, Cenozoic mean 0.789). In contrast with the majority of taxa, the originations and extinctions of index taxa, as well as of other taxa belonging to biostratigraphically important systematic groups, seems to be continuous.