Theoretical and numerical results of a stochastic model describing resistance and non-resistance strains of influenza

Abstract

In this world, there are several acute viral infections. One of them is influenza, a respiratory disease caused by the influenza virus. Stochastic modelling of infectious diseases is now a popular topic in the current century. Several stochastic epidemiological models have been constructed in the research papers. In the present article, we offer a stochastic two-strain influenza epidemic model that includes both resistant and non-resistance strains. We demonstrate both the existence and uniqueness of the global positive solution using the stochastic Lyapunov function theory. The extinction of our research sickness results from favourable circumstances. Additionally, the infection’s persistence in the mean is demonstrated. Finally, to demonstrate how well our theoretical analysis performs, various noise disturbances are simulated numerically.

Insights into COVID-19 stochastic modelling with effects of various transmission rates: simulations with real statistical data from UK, Australia, Spain, and India

“…For example, Raja et al demonstrated nonsingular heat conduction equation under SDE [20]. In recent years, models of epidemics have been examined using SDEs, including those related to Hepatitis B disease [21,22], influenza disease [23], dengue transmission [24], co-infection model [25] and COVID-19 models [26][27][28].…”

Stochastic Extension of a Two-Strain SIR Model with Non-Monotone Incidence Functions: Analysis of Stochastic Thresholds and Disease Dynamics

“…Huang et al [12] presented an advanced stochastic SIRS model with two types of nonlinear incidence rates. Finally, Farah et al conducted a study on a stochastic model of two influenza strains with both bilinear and saturated incidence rates [8].…”

Stochastic analysis of two‐strain epidemic model with non‐monotone incidence rates: Application to COVID‐19 pandemic

“…In recent times, there have been several attempts to describe epidemics with two strains or two different types of infectious diseases by using stochastic epidemic model [44][45][46][47][48][49]. Among these previously mentioned models, we distinct the use of two distinct incidence functions one with a bilinear incidence rate and the other with a saturated incidence rate [44,45], both saturated incidence rates [46,47], one with bilinear incidence rate and the other with nonmonotonic incidence rates [48], and both Beddington-DeAngelis incidence rates [49]. The authors of all the stochastic epidemic models mentioned above demonstrate the extinction and persistence in mean, and subsequently verify their theoretical findings through numerical simulations.…”

“…Researchers using the stochastic models have achieved more valuable results since they can build up a distribution of the predicted results multiple times, compared with one single predicted value of the deterministic model. In recent times, there have been several attempts to describe epidemics with two strains or two different types of infectious diseases by using stochastic epidemic model [44][45][46][47][48][49]. Among these previously mentioned models, we distinct the use of two distinct incidence functions one with a bilinear incidence rate and the other with a saturated incidence rate [44,45], both saturated incidence rates [46,47], one with bilinear incidence rate and the other with nonmonotonic incidence rates [48], and both Beddington-DeAngelis incidence rates [49].…”