Abstract. In this paper, we study a class of multi-group SIRS epidemic models with nonlinear incidence rate which have cross patch infection between different groups. The basic reproduction number R0 is calculated. By using the method of Lyapunov functions, LaSalle’s invariance principle, the theory of the nonnegative matrices and the theory of the persistence of dynamical systems, it is proved...

A Berge copy of a graph is hypergraph obtained by enlarging the edges arbitrarily. Grósz, Methuku and Tompkins in 2020 showed that for any F, there an integer r0=r0(F), such r?r0, r-uniform without F has o(n2) hyperedges. The smallest r0 called uniformity threshold denoted th(F). They th(F)?R(F,F?), where R denotes off-diagonal Ramsey number F? form deleting edge. We improve this bound to th(F)...

of Controlled Sequential Bifurcation for Simulation Factor Screening A. Appendix: Proofs A.1. Proof of Lemma 1 For a group {k1, k1 + 1, . . . , k2} with group effect ζ = ∑k2 k1+1 βi, an arbitrary sample path is SPr0(r) = ∑r `=1(D`(k1, k2)− r0), r = N0, N0 + 1, . . .. If r′ 0 < r0, then for every sample path, SPr′ 0(r) > SPr0(r) for all r. Thus, every sample path that is classified as unimportan...

BACKGROUND In 2015, the Zika arbovirus (ZIKV) began circulating in the Americas, rapidly expanding its global geographic range in explosive outbreaks. Unusual among mosquito-borne diseases, ZIKV has been shown to also be sexually transmitted, although sustained autochthonous transmission due to sexual transmission alone has not been observed, indicating the reproduction number (R0) for sexual t...

Some analytical results are given for a model that describes the propagation of a disease in a population of individuals who travel between n cities. The model is formulated as a system of 2n ordinary differential equations with terms accounting for disease transmission, recovery, birth, death, and travel between cities. The mobility component is represented as a directed graph with cities as v...

In this paper a mosquito-borne parasitic infection model in periodic environment is considered. Threshold parameter R0 is given by linear next infection operator, which determined the dynamic behaviors of system. We obtain that when R0 < 1, the disease-free periodic solution is globally asymptotically stable and when R0 > 1 by Poincaré map we obtain that disease is uniformly persistent. Numeric...

A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium ap...

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number R0 are identified and its threshold properties are discussed. When R0<1, the infection-free equilibrium E0 is globally asymptotic...

To examine the neuroprotective effects of ginsenoside R0, we investigated the effects of ginsenoside R0 in PC12 cells under an anoxic or oxidative environment with Edaravone as a control. PC12 neuroendocrine cells were used as a model target. Anoxic damage or oxidative damage in PC12 cells were induced by adding sodium dithionite or hydrogen peroxide respectively in cultured medium. Survival ra...

of Controlled Sequential Bifurcation for Simulation Factor Screening A. Appendix: Proofs A.1. Proof of Lemma 1 For a group {k1, k1 + 1, . . . , k2} with group effect ζ = ∑k2 k1+1 βi, an arbitrary sample path is SPr0(r) = ∑r `=1(D`(k1, k2)− r0), r = N0, N0 + 1, . . .. If r′ 0 < r0, then for every sample path, SPr′ 0(r) > SPr0(r) for all r. Thus, every sample path that is classified as unimportan...