Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

5siThe lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-Vaccinated- Latent-Infectious-Removed) model of infectious disease transmission, where vacci- nated individuals are also susceptible, although to a lesser degree. Using Lyapunov- Lasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever Rvac > 1 . Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.openopenNkamba, L. N.; Ntaganda, J. M.; Abboubakar, H.; Kamgang, J. C.; Castelli, LorenzoNkamba, L. N.; Ntaganda, J. M.; Abboubakar, H.; Kamgang, J. C.; Castelli, Lorenz

Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

Abstract We develop and analyse a deterministic population-based ordinary differential equation of malaria transmission to consider the impact of three common assumptions of malaria models: (1) malaria infection does not change the attractiveness of humans to mosquitoes; (2) exposed mosquitoes (infected with malaria but not yet infectious to humans) have the same biting rate as susceptible mosquitoes; and (3) mosquitoes infectious to humans have the same biting rate as susceptible mosquitoes. We calculate the basic reproductive number, $$R_0$$ R 0 , for this model and show the existence of a transcritical bifurcation at $$R_0=1$$ R 0 = 1 , in common with most epidemiological models. We further show that for some sets of parameter values, this bifurcation can be backward (subcritical). We show with numerical simulations that increasing the relative attractiveness of infectious humans, increases $$R_0$$ R 0 but reduces the equilibrium prevalence of infectious humans; decreasing the biting rate of exposed mosquitoes increases $$R_0$$ R 0 and the equilibrium prevalence of infectious humans and mosquitoes; and increasing the biting rate of infectious mosquitoes has no impact on $$R_0$$ R 0 or the equilibrium prevalence of infectious humans, but decreases the infectious prevalence of infectious mosquitoes. These analyses of a simple malaria model show that common assumptions around the relative attractiveness of infectious humans and the relative biting rates of exposed and infectious mosquitoes can have substantial and counter-intuitive effects on malaria transmission dynamics

Erratum to: modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans

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Fractional modeling of Hansen's disease (Leprosy) transmission dynamics

International audienceIn this work, we study a mathematical model for the Hansen's disease (leprosy) transmission dynamics with both integer and fractional derivatives in the Caputo sense. After the model formulation, we compute the leprosy reproduction number R 0 and prove the existence of two steady states named the Leprosy-free equilibrium and the leprosy-endemic equilibrium which exists and is unique if and only if R 0 > 1. Using the general theory of Lyapunov, we prove the global asymptotic stability of both steady states, for both models. The existence and uniqueness of the solutions of the fractional model are proved using fixed point theory. We finally perform numerical simulations to validate our analytical results, as well as to evaluate the impact of varying the fractional-order parameter on the disease dynamics

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explic- itly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the e ectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of e ective vaccination (i.e. 3 doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.South African Research Chairs Initiatives (SARChI Chair), in Mathematical Models and Methods in Bioengineering and Biosciences.http://www.elsevier.com/locate/msec2017-08-31hb2016Mathematics and Applied Mathematic