Authors: Samuel Bowong ¹; Jean-Luc Dimi ²; Jean-Claude Kamgang ³; Joseph Mbang ⁴; Jean Jules Tewa ⁵

• 1 Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
• 2 Department of mathematics [Brazzaville]
• 3 Département de Mathématiques et Informatique [Univ Ngaoundéré]
• 4 Département de Mathématiques Université de Yaoundé 1 = Department of Mathematics [Yaoundé, Cameroon]
• 5 National Advanced School of Engineering

We present the recent results obtained for the within-host models of malaria and HIV. We briefly recall the Anderson-May-Gupter model. We also recall the Van Den Driessche method of computation for the basic reproduction ratio R0 ; here, a very simple formula is given for a new class of models. The global analysis of these models can be founded in [1, 2, 3, 5]. The results we recall here are for a model of one strain of parasites and many classes of age, a general model of n strains of parasites and k classes of age, a S E1 E2 · · ·En I S model with one linear chain of compartments and finally a general S Ei1 Ei2 · · ·Ein I S model with k linear chains of compartments. When R0 <=1, the authors prove that there is a trivial equilibria calling disease free equilibrium (DFE) which is globally asymptotically stable (GAS) on the non-negative orthant , and when R0 > 1, they prove the existence of a unique endemic equilibrium in the non-negative orthant and give an explicit formula. They provided a weak condition for the global stability of endemic equilibrium