Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate

Abstract

In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by a seasonal forcing function that takes into account the variability of the climate. We introduce a generalized force of infection function to study different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, we obtain sufficient conditions that guarantee the existence of a positive periodic solution. Moreover, we provide sufficient conditions that assure the global attractivity of the positive periodic solution. Numerical results corroborate the theoretical results in the sense that the solutions are positive and the periodic solution is a global attractor. This type of models are important, since they take into account the variability of the weather and the impact on some epidemics such as the current COVID-19 pandemic.

A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters

“…Moreover, in numerical simulations large outbreaks have been observed even when R 0 was below the threshold value 1 Bacaër and Gomes (2009); ?. Since then, the computation and interpretation of an appropriate formula for R 0 for non-autonomous systems have attracted much attention Arenas et al (2021); Bacaër (2007); Nakata and Kuniya (2010).…”

“…On the other hand, there exist different modelling studies on the seasonality of several other infectious diseases (influenza, measles, chickenpox, pertussis, malaria etc.) or epidemiological models with a generic aspect Arenas et al (2021); Chitnis et al (2012); Doutor et al (2016); Greer et al (2020); Onyango and Müller (2013); Soper (1929); Stone et al (2007).…”

A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters

“…Since IMD displays temporary outbreaks rather than stable epidemics all over the world except the meningitis belt, a non-autonomous system may better explain the seasonal exacerbation of the disease. Inspired by this idea, an age-structured model driven by a seasonal forcing function was introduced in [ 34 ] that takes into account the variability of the climate describing the transmission dynamics between children and adults, where the authors obtained sufficient conditions that assure the existence and global attractivity of a positive periodic solution. In the present paper, we concentrate on the stability of the disease-free state in the time-dependent transmission case and show that the mean values of transmission functions enable to define the exacerbation of IMD as an outbreak.…”

“…On the other hand, there exist modelling studies on the seasonality of several other infectious diseases (influenza, measles, chickenpox, pertussis, malaria, etc.) or epidemiological models with a generic aspect [ 28 – 34 ].…”

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

“…Thus, under certain conditions (for instance only individuals in the S(t) class can get infected) R t = R 0 S(t)/N, which relates the value of the virus transmissibility β to the effective reproduction number (for more details see [31,78,79]). In addition, in this section we study the global stability of these equilibrium points using some suitable Lyapunov functionals [43,[80][81][82][83][84][85].…”