A model incorporating combined RTIs and PIs therapy during early HIV-1 infection.

We develop a within host mathematical model of HIV-1 infection describing the effects of combined RTIs and PIs treatments on early HIV-1 infection when treatment is captured using periodic functions of pharmacokinetics type. We use an alternative of the basic reproduction number to analyze endemicity level of HIV-1 infection. Various treatment scenarios incorporating perfect and imperfect drug adherence in drug administration are explored. Our results show that pharmacokinetics treatment is a more realistic way of administering the treatment. Apart from confirming that PIs drugs are more effective than RTIs drugs and that combined RTIs and PIs therapy is more effective than monotherapy of RTIs or PIs, our results show that imperfect drug adherence leads to the increase of viral in the absence of mutation even though the drug is good.

A two-age-classes dengue transmission model.

In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.