title: Optimal control of a malaria model with asymptomatic class and superinfection.
abstract: In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individuals recover and move to the susceptible class. The basic reproduction number, R0, is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R0<1, and may have up to four endemic equilibria. The model exhibits backward bifurcation generated by two mechanisms; standard incidence and superinfection. If the model does not allow for superinfection or deaths due to the disease, then DFE is globally stable which suggests that backward bifurcation is no longer possible. Simulations suggest that total prevalence of malaria is the highest if all individuals show symptoms upon infection, but then undergoes an incomplete treatment and the lowest when all the individuals first move to the symptomatic class then treated successfully. Total prevalence is average if more individuals upon infection move to the asymptomatic class. We study optimal control strategies applied to bed-net use and treatment as main tools for reducing the total number of symptomatic and asymptomatic individuals. Simulations suggest that the optimal control strategies are very dynamic. Although they always lead to decrease in the symptomatic infectious individuals, they may lead to increase in the number of asymptomatic infectious individuals. This last scenario occurs if a large portion of newly infected individuals move to the symptomatic class but many of them do not complete treatment or if they all complete treatment but the superinfection rate of asymptomatic individuals is average.
authors.affiliation: College of Mathematics and Statistic Science, Xinyang Normal University, Xinyang, 46400, CHINA. Electronic address: limingcai@amss.ac.cn.
authors.forename: Liming
authors.initials: L
authors.lastname: Cai
authors.affiliation: College of Mathematics and information Science, Xinyang Normal University, Xinyang, 46400, CHINA.
authors.forename: Xuezhi
authors.initials: X
authors.lastname: Li
authors.affiliation: Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA. Electronic address: ntuncer@fau.edu.
authors.forename: Necibe
authors.initials: N
authors.lastname: Tuncer
authors.affiliation: Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, United States. Electronic address: maia@ufl.edu.
authors.forename: Maia
authors.initials: M
authors.lastname: Martcheva
authors.affiliation: Department of Mathematics, Stockholms University, SE-106 91 Stockholm, Sweden.
authors.forename: Abid Ali
authors.initials: AA
authors.lastname: Lashari
mesh_terms: D058345:Asymptomatic Infections / Q000453:epidemiology; D050936:Basic Reproduction Number; D006801:Humans; D015994:Incidence; D008288:Malaria / Q000453:epidemiology / Q000469:parasitology*; D008954:Models, Biological; D015995:Prevalence; D015163:Superinfection / Q000453:epidemiology
keywords: Asymptomatic individuals; Backward bifurcation; Basic reproduction number; Mosquito-borne diseases; Optimal control strategies; Stability