Modeling and analysis of the symptomatic and asymptomatic infections of swine flu with optimal control

A Mathematical Model of the Tuberculosis Epidemic

Tuberculosis has continued to retain its title as "the captain among these men of death". This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I₁, diagnosed infectious I₂, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity [Formula: see text] is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0-20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.

Mathematical modeling and analysis for controlling the spread of infectious diseases

In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.