Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .

Global dynamics analysis for a nonlinear HTLV-I model with logistic proliferation and CTL response

It is beyond dispute that cytotoxic T-lymphocytes(CTLs)exert a vital function in the host's antiviral defense mechanism.With the idea of the above factor and the logistic proliferation of CD4+T-cells,we establish a HTLV-I(human T-cell leukemia virus type-I)mathematical model.First,two threshold parameters Ro and Re(the basic reproduction numbers for viral infection and CTL immune response,respectively)are obtained.Second,sufficient criteria for local and global asymptotic stabilities of the feasible equilibria of the model are deduced,respectively.Third,the sensitivity analyses of Ro and Rc are performed to better understand the effective strategies for HTLV-I infection.Finally,not only numerical simulations are given to illustrate the stability conclusions,but also the biological significance is stated.

Hopf bifurcation of a delay SIRS epidemic model with novel nonlinear incidence:Application to scarlet fever

An SIRS epidemic model incorporating incubation time delay and novel nonlinear incidence is proposed and analyzed to seek for the control strategies of scarlet fever,where the contact rate which can reflect the regular behavior and habit changes of children is non-monotonic with respect to the number of susceptible.The model without delay may exhibit backward bifurcation and bistable states even though the basic reproduction number is less than unit.Furthermore,we derive the conditions for occurrence of Hopf bifurcation when the time delay is considered as a bifurcation parameter.The data ofscarlet fever of China are simulated to verify our theoretical results.In the end,several effective preventive and intervention measures of scarlet fever are found out.

Survival analysis of an impulsive stochastic facultative mutualism system with saturation effect

A system of impulsive stochastic differential equations is proposed as a two-species facultative mutualism model subject to impulsive and two coupling noise source perturbations,in which the saturation effect is taken into account.A set of sufficient criteria for extinction(exponential extinction and extinction)and permanence(permanence in time average and stochastic permanence)of the system are established.Extensive simulation figures are demonstrated to support the theoretical findings.Meanwhile,we look at the effects of coupling white noises,impulses,intrinsic growth rates,intra-specific competition rates and inter-specific mutualism rates on the survival of populations.

Global dynamics and optimal control of an influenza model with vaccination, media coverage and treatment

In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Purthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.