Mathematical modelling of the effects of peer-educators’ campaign on the dynamics of HIV/AIDS in Rwanda

In this paper, we analyse the effects of peer-educator’s campaign on the dynamics of HIV. We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which help to account for a time delay due to incubation period of infective before developing AIDS. The sex-structured HIV/AIDS model divides the population into two subpopulations, namely; females and males. Both disease Free equilibrium and the endemic equilibrium points for the model are determined and their stability are examined. The model is extended to assess the effect of peer- educational campaigns in slowing or eradicating the epidemic. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of each intervention in a community. The models are numerically analyzed to assess the effectiveness of the treatment free measure, namely; peer educational campaign on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters of Rwanda. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of educational campaigns as a preventive strategy in a heterosexually active populationMathematics Subject classifications (MSC 2010): 34D20, 34K60, 92D25, 34K25, 34K28Keywords: Population dynamics, Stability, Basic reproductive numbers, Equilibriu

Characterising two-pathogen competition in spatially structured environments

Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space structure of the population. Here we focus on the competition between two acute infections and we address the role of host mobility and cross-immunity in shaping possible dominance/co-dominance regimes. Host mobility is modelled as a network of traveling flows connecting nodes of a metapopulation, and the two-pathogen dynamics is simulated with a stochastic mechanistic approach. Results depict a complex scenario where, according to the relation among the epidemiological parameters of the two pathogens, mobility can either be non-influential for the competition dynamics or play a critical role in selecting the dominant pathogen. The characterisation of the parameter space can be explained in terms of the trade-off between pathogen's spreading velocity and its ability to diffuse in a sparse environment. Variations in the cross-immunity level induce a transition between presence and absence of competition. The present study disentangles the role of the relevant biological and ecological factors in the competition dynamics, and provides relevant insights into the spatial ecology of infectious diseases.Comment: 30 pages, 6 figures, 1 table. Final version accepted for publication in Scientific Report

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits : A bifurcation analysis

Altres ajuts: CERCA Programme/Generalitat de CatalunyaWe investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov-Takens and zero- Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner

MSEICR Fractional Order Mathematical Model of The Spread Hepatitis B

This research aims to develop the MSEICR model by reviewing fractional orders on the spread of Hepatitis B by administering vaccinations and treatment, and analyzing fractional effects by numerical simulations of the MSEICR mathematical model using the method Grunwald Letnikov. Researchers use qualitative methods to achieve the object of research. The steps are to determine the MSEICR model by reviewing the fractional order, looking for endemic equilibrium points for each non-endemic and endemic equilibrium point, determining the equality of characteristics and eigenvalues ​​of the Jacobian matrix. Next, look for values  ​​(Basic Reproductive Numbers), analyze stability around non-endemic and endemic equilibrium points and complete numerical simulations. From the simulation provided, it is known that by giving a fractional alpha value of and  , the greater the value of the fractional order parameters used, the movement of the solution graphs is getting closer to the equilibrium point. If given and still endemic, whereas if and  the value  is increased to non-endemic, then the number of hepatitis B sufferers will disappear

Modelling the Hepatitis C with Different Types of Virus Genome

Hepatitis C virus (HCV) is one of the leading known causes of liver disease in the world. The HCV is a single-stranded RNA virus. The genomes of HCV display significant sequence heterogeneity and have been classified into types and subtypes. Types from 1 to 11 have so far been recognized, each type having a variable number of subtypes. It has been confirmed that 90% approximately of the isolates HCV infections in Egypt belong to a single subtype (4a) [10]. In this paper, we construct a mathematical model to study the spread of HCV-subtype 4a amongst the Egyptian population. The relation between HCV-subtype 4a and the other subtypes has also been studied. The values of reproduction numbers R01, R02 have been derived [5]. Also, threshold conditions for the value of the transmission rates k1 and k02, in terms of R01, R02 and the mutation factor μ have been determined to insure that the disease will die out. If the conditions fail to happen the disease takes off and becomes endemic