RESUMO
Hosts can activate a defensive response to clear the parasite once being infected. To explore how host survival and fecundity are affected by host-parasite coevolution for chronic parasitic diseases, in this paper, we proposed an age-structured epidemic model with infection age, in which the parasite transmission rate and parasite-induced mortality rate are structured by the infection age. By use of critical function analysis method, we obtained the existence of the host immune evolutionary singular strategy which is a continuous singular strategy (CSS). Assume that parasite-induced mortality begins at infection age [Formula: see text] and is constant v thereafter. We got that the value of the CSS, [Formula: see text], monotonically decreases with respect to infection age [Formula: see text] (see Case (I)), while it is non-monotone if the constant v positively depends on the immune trait c (see Case (II)). This non-monotonicity is verified by numerical simulations and implies that the direction of immune evolution depends on the initial value of immune trait. Besides that, we adopted two special forms of the parasite transmission rate to study the parasite's virulence evolution, by maximizing the basic reproduction ratio [Formula: see text]. The values of the convergence stable parasite's virulence evolutionary singular strategies [Formula: see text] and [Formula: see text] increase monotonically with respect to time lag L (i.e., the time lag between the onset of transmission and mortality). At the singular strategy [Formula: see text] and [Formula: see text], we further obtained the expressions of the case mortalities [Formula: see text] and how they are affected by the time lag L. Finally, we only presented some preliminary results about host and parasite coevolution dynamics, including a general condition under which the coevolutionary singular strategy [Formula: see text] is evolutionarily stable.
Assuntos
Parasitos , Animais , Virulência , Conceitos Matemáticos , Modelos Biológicos , Número Básico de ReproduçãoRESUMO
COVID-19 is a disease caused by infection with the virus 2019-nCoV, a single-stranded RNA virus. During the infection and transmission processes, the virus evolves and mutates rapidly, though the disease has been quickly controlled in Wuhan by 'Fangcang' hospitals. To model the virulence evolution, in this paper, we formulate a new age structured epidemic model. Under the tradeoff hypothesis, two special scenarios are used to study the virulence evolution by theoretical analysis and numerical simulations. Results show that, before 'Fangcang' hospitals, two scenarios are both consistent with the data. After 'Fangcang' hospitals, Scenario I rather than Scenario II is consistent with the data. It is concluded that the transmission pattern of COVID-19 in Wuhan obey Scenario I rather than Scenario II. Theoretical analysis show that, in Scenario I, shortening the value of L (diagnosis period) can result in an enormous selective pressure on the evolution of 2019-nCoV.
Assuntos
COVID-19 , China/epidemiologia , Humanos , Modelos Biológicos , SARS-CoV-2 , VirulênciaRESUMO
We propose a model of a joint spread of heroin use and HIV infection. The unique disease-free equilibrium always exists and it is stable if the basic reproduction numbers of heroin use and HIV infection are both less than 1. The semi-trivial equilibrium of HIV infection (heroin use) exists if the basic reproduction number of HIV infection (heroin use) is larger than 1 and it is locally stable if and only if the invasion number of heroin use (HIV infection) is less than 1. When both semi-trivial equilibria lose their stability, a coexistence equilibrium occurs, which may not be unique. We compare the model to US data on heroin use and HIV transmission. We conclude that the two diseases in the US are in a coexistence regime. Elasticities of the invasion numbers suggest two foci for control measures: targeting the drug abuse epidemic and reducing HIV risk in drug-users.
Assuntos
Coinfecção/epidemiologia , Infecções por HIV/complicações , Infecções por HIV/epidemiologia , Dependência de Heroína/complicações , Dependência de Heroína/epidemiologia , Número Básico de Reprodução , Simulação por Computador , Humanos , Modelos Biológicos , Análise Numérica Assistida por Computador , Estados Unidos/epidemiologiaRESUMO
Based on the development of heroin vaccine, in this paper, we propose an age structured heroin transmission model with treatment and vaccination. The model allows the drug reuse rate of the individuals in treatment to depend on a treatment-age and the vaccine waning rate of the vaccinated to depend on a vaccination age. Meanwhile, the model allows that the heroin vaccine provides an imperfect protection (i.e., the vaccinated individuals can also become drug addicted). We derive the basic reproduction number which dependents on vaccination. The basic reproduction number completely determines the persistence and extinction of heroin spread, i.e., if the basic reproduction number is less than one the drug-free steady state is globally asymptotically stable (i.e., the heroin spread dies out), if the basic reproduction number is larger than one, there exists an unique positive steady state and it is locally and globally stable in some special cases. Finally, some numerical simulations are carried out to illustrate the stability of the positive steady state.