The novel coronavirus disease (COVID-19) has resulted in an ongoing pandemic affecting the health system and economy of more than 200 countries worldwide. Mathematical models are used to predict the biological and epidemiological tendencies of an epidemic and to develop methods for controlling it. In this work, we use a mathematical model perspective to study the role of behavior change in slowing the spread of COVID-19 in Saudi Arabia. The real-time updated data from March 2, 2020, to January 8, 2021, were collected from the Saudi Ministry of Health, aiming to provide dynamic behaviors of the epidemic in Saudi Arabia. During this period, 363,692 people were infected, resulting in 6293 deaths, with a mortality rate of 1.73%. There was a weak positive relationship between the spread of infection and mortality
R
2
=
0.459
. We used the susceptible-exposed-infection-recovered (SEIR) model, a logistic growth model, with a special focus on the exposed, infected, and recovered individuals to simulate the final phase of the outbreak. The results indicate that social distancing, hygienic conditions, and travel limitations are crucial measures to prevent further spread of the epidemic.
Investigations are undertaken into simple predator–prey models with rational interaction terms in one and two spatial dimensions. Focusing on a case with linear interaction and saturation, an analysis for long domains in 1D is undertaken using ideas from spatial dynamics. In the limit that prey diffuses much more slowly than predator, the Turing bifurcation is found to be subcritical, which gives rise to localized patterns within a Pomeau pinning parameter region. Parameter regions for localized patterns and isolated spots are delineated. For a realistic range of parameters, a temporal Hopf bifurcation of the balanced equilibrium state occurs within the localized-pattern region. Detailed spectral computations and numerical simulations reveal how the Hopf bifurcation is inherited by the localized structures at nearby parameter values, giving rise to both temporally periodic and chaotic localized patterns. Simulation results in 2D confirm the onset of complex spatio-temporal patterns within the corresponding parameter regions. The generality of the results is confirmed by showing qualitatively the same bifurcation structure within a similar model with quadratic interaction and saturation. The implications for ecology are briefly discussed.
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