A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied. The force of infection is of proportionate mixing type. A threshold sigma is identified which determines the outcome of the disease; if sigma < or = 1, the infected fraction of the population disappears so the disease dies… (More)
A mathematical model that describes HIV infection of CD4(+) T cells is analyzed. Global dynamics of the model is rigorously established. We prove that, if the basic reproduction number R(0) < or = 1, the HIV infection is cleared from the T-cell population; if R(0) > 1, the HIV infection persists. For an open set of parameter values, the chronic-infection… (More)
Various eeects of disease caused death on the host population is studied in an epidemic model of SIR type. The exponential rate for natural birth and death is assumed to be equal so that the total population is balanced in the absence of the disease. The model has the surprising feature that it requires a simple mathematical analysis while revealing… (More)
We study a population model for an infectious disease that spreads in the host population through both horizontal and vertical transmission. The total host population is assumed to have constant density and the incidence term is of the bilinear mass-action form. We prove that the global dynamics are completely determined by the basic reproduction number R 0… (More)
A necessary and sufficient condition for the stability of n = n matrices with real entries is proved. Applications to asymptotic stability of equilibria for vector fields are considered. The results offer an alternative to the well-known Routh᎐Hurwitz conditions.
A symmetric BAM neural network model with delay is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. The existence of multiple periodic solutions is established using a symmetric Hopf bifurcation result of Wu [J. Wu, Symmetric functional differential equations and neural networks with… (More)
Disabilities after neural injury, such as stroke, bring tremendous burden to patients, families and society. Besides the conventional constrained-induced training with a paretic arm, bilateral rehabilitation training involves both the ipsilateral and contralateral sides of the neural injury, fitting well with the fact that both arms are needed in common… (More)
Falls are common in older adults and result in adverse outcomes. Impaired mobility and poor muscle strength have been consistently identified as the main contributors to falls. We choose three easy-to-perform tests (i.e. Timed Up and Go test (TUGT), walking speed (WS) and grip strength (GS)) in order to assess mobility and muscle strength to further define… (More)