We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number R0 is calculated. For R0 < 1...

We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) strains. Drug resistance first emerges when strains mutate become drug-resistant, possibly as consequence inadequate treatment, i.e. amplification. In this case, are coupled. perform dynamical analysis resulting system find that contains three equilibrium points...

Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart the spread of SARS-CoV-2 virus are analyzed compared. For version model, conditions stability disease-free equilibrium derived and, in addition, existence bifurcation state related to endemic established. extinction persistence mean disease derived. Complete sensitivity analysis thresholds between mean-pers...

Recently, a continuous-time compartmental mathematical model for the spread of Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and local stability Disease Free Equilibrium (DFE) analysed. Here, we propose an analogous discrete-time and, using suitable Lyapunov function, prove global DFE point. Using COVID-19 real data, show, through num...

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff’s matrix tree theorem...

-The disease dynamics and progression of HIV-MTCT over a period of time and disease transmission and susceptible simulation model (DTSM-MODEL) were computed by different reproduction numbers for each time interval with set of fixed values of the parameters. As per the model, study found that placental absorption ,prolonged breast feeding and absence of ARV at the onset of birth or delivery, aft...

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidem...

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain new threshold value (R0m) through the Stratonovich differential equation, different from usual basic reproduction number. If R0m&lt;1, disease-free equilibrium of illness is globally asymptotically stable in probability one. R0m&gt;1, disease permanent mean one has an endemic st...

We analyze a mathematical model for infectious diseases that progress through distinct stages within infected hosts. An example of such a disease is AIDS, which results from HIV infection. For a general n-stage stage-progression (SP) model with bilinear incidences, we prove that the global dynamics are completely determined by the basic reproduction number R0: If R(0) =/< 1; then the disease-fr...

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 R0(p, q), where p and q are fractions of ...