(R1522) Modelling the Influence of Desertic Aerosols on the Transmission Dynamics of Neisseria Meningitidis Serogroup A

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use it to investigate the existence and stability of equilibria. In this regard, we prove that the model undergoes a backward bifurcation phenomenon. We highlight the detrimental impact of aerosol dust by showing that its inhalation augments the reproduction number and enhances the endemic level of NmA.We also highlight the favorable role of vaccine in eliminating the disease when it has a high level of efficacy and is used to protect a large proportion of the population. The theoretical results are supported and illustrated by numerical simulations

Global stability analysis of a metapopulation SIS epidemic model

International audienceThe conjecture of Arino and van den Driessche (2003) that a SIS type model in a mover- stayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R0 ≤ 1, then the disease free equilibrium is globally asymptotically sta- ble. If R0 > 1, then there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative orthant minus the stable manifold of the disease free equilibrium

Metapopulation SIS epidemic model

International audienceWe consider a metapopulation model with $n$ patches. The migration model is with residents and travelers. The epidemic model is of SIS type. We confirm the conjecture of Arino and van den Driessche. We prove that if $\mathcal R_0 \leq 1$ then the disease free equilibrium is globally asymptotically stable. If $\mathcal R_0 >1$ we prove that there exists a unique endemic equilibrium which is globally asymptotically stable on the nonnegative orthant except the disease free equilibrium

Global stability of a two-patch cholera model with fast and slow transmissions

Please read abstract in the article.The Abdus Salam International Center for Theoretical Physics (ICTP) in Trieste-Italy under the Associateship Scheme, the African Center of Excellence in Information and Communication Technologies (CETIC) in Cameroon and the South African Research Chairs Initiative (SARChI Chair), in Mathematical Models and Methods in Bioengineering and Biosciences.http://www.elsevier.com/locate/matcomhj2021Mathematics and Applied Mathematic

Avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment

In this paper, an avian–human influenza epidemic model with diffusion, nonlocal delay and spatial homogeneous environment is investigated. This model describes the transmission of avian influenza among poultry, humans and environment. The behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions is investigated. By means of linearization method and spectral analysis the local asymptotical stability is established. The global asymptotical stability for the poultry sub-system is studied by spectral analysis and by using a Lyapunov functional. For the full system, the global stability of the disease-free equilibrium is studied using the comparison Theorem for parabolic equations. Our result shows that the disease-free equilibrium is globally asymptotically stable, whenever the contact rate for the susceptible poultry is small. This suggests that the best policy to prevent the occurrence of an epidemic is not only to exterminate the asymptomatic poultry but also to reduce the contact rate between susceptible humans and the poultry environment. Numerical simulations are presented to illustrate the main results.http://www.elsevier.com/locate/nonrwahj2023Mathematics and Applied Mathematic

Assessing the impact of the environmental contamination on the transmission of Ebola virus disease (EVD)

Please read abstract in the article.The first (T.B.) and the third (J.L.) authors are grateful to the South African Research Chairs Initiative (SARChI Chair), in Mathematical Models and Methods in Bioengineering and Biosciences. The first (T.B.) and the second (S.B.) authors acknowledge the support of Center of Excellence Cameroon (CETIC).https://link.springer.com/journal/121902018-10-01hj2018Mathematics and Applied Mathematic

Prevalence-based modeling approach of schistosomiasis : global stability analysis and integrated control assessment

A system of nonlinear differential equations is proposed to assess the effects of prevalence-dependent disease contact rate, pathogen’s shedding rates, and treatment rate on the dynamics of schistosomiasis in a general setting. The decomposition techniques by Vidyasagar and the theory of monotone systems are the main ingredients to deal completely with the global asymptotic analysis of the system. Precisely, a threshold quantity for the analysis is derived and the existence of a unique endemic equilibrium is shown. Irrespective of the initial conditions, we prove that the solutions converge either to the disease-free equilibrium or to the endemic equilibrium, depending on whether the derived threshold quantity is less or greater than one. We assess the role of an integrated control strategy driven by human behavior changes through the incorporation of prevalence-dependent increasing the prophylactic treatment and decreasing the contact rate functions, as well as the mechanical water sanitation and the biological elimination of snails. Because schistosomiasis is endemic, the aim is to mitigate the endemic level of the disease. In this regard, we show both theoretically and numerically that: the reduction of contact rate through avoidance of contaminated water, the enhancement of prophylactic treatment, the water sanitation, and the removal of snails can reduce the endemic level and, to an ideal extent, drive schistosomiasis to elimination.The University of Pretoria Senior Postdoctoral Program Grant.https://www.springer.com/journal/403142022-01-20hj2021Mathematics and Applied Mathematic

A metapopulation model for the population dynamics of anopheles mosquito

Please read abstract in the article.This article was co-written by B. Tsanou before he joined the University of Pretoria.http://www.elsevier.com/ locate/amchj2021Mathematics and Applied Mathematic

Dynamics of host-reservoir transmission of Ebola with spillover potential to humans

Ebola virus disease (EVD) is a zoonotic borne disease (i.e. disease that is spread from animals to people). Therefore human beings can be infected through direct contact with an infected animal (fruit-eating bat or great ape). It has been demonstrated that fruit-eating bats of pteropodidae family are potential reservoir of EVD. Moreover, it has been biologically shown that fruit-eating bats do not die due to EVD and bear the Ebola viruses lifelong. We develop in this paper, a mathematical model to assess the impact of the reservoir on the dynamics of EVD. Our model couples a bat-to-bat model with a human-to-human model and the indirect environmental contamination through a spillover process (i.e. process by which a zoonotic pathogen moves (regardless of transmission mode) from an animal host (or environmental reservoir) to a human host) from bats to humans. The sub-models and the coupled models exhibit each a threshold behavior with the corresponding basic reproduction numbers being the bifurcation parameters. Existence of equilibria, their global stability are established by combining monotone operator theory, Lyapunov-LaSalle techniques and graph theory. Control strategies are assessed by using the target reproduction numbers. The efforts required to control EVD are assessed as well through S-control. The spillover event is shown to be highly detrimental to EVD by allowing the disease to switch from bats to humans even though the disease was not initially endemic in the human population. Precisely, we show that the spillover phenomenon contributes to speed up the disease outbreak. This suggests that the manipulation and consumption of fruit-bats play an important role in sustaining EVD in a given environment